VOCATIONAL 
MATHEMATICS 

FOR  GIRLS 


BY 
WILLIAM    H.    DOOLEY 

AUTHOR  OF  "VOCATIONAL  MATHEMATICS 
"TEXTILES,"  ETC. 


D.    C.    HEATH   &   CO.,   PUBLISHERS 
BOSTON  NEW  YORK  CHICAGO 


COPYRIGHT,  1917, 
BY  D.  C.  HEATH  &  Co. 

IB? 


PREFACE 

THE  author  has  had,  during  the  last  ten  years,  considerable 
experience  in  organizing  and  conducting  intermediate  and  sec- 
ondary technical  schools  for  boys  and  girls.  During  this  time 
he  has  noticed  the  inability  of  the  average  teacher  in  mathe- 
matics to  give  pupils  practical  applications  of  the  subject. 
Many  teachers  are  not  familiar  with  the  commercial  and  rule 
of  thumb  methods  of  solving  mathematical  problems  of  every- 
day life.  Too  often  a  girl  graduates  from  the  course  in  mathe- 
matics without  being  able  to  "  commercialize  "  or  apply  her 
mathematical  knowledge  in  such  a  way  as  to  meet  the  needs 
of  trade,  commerce,  and  home  life. 

It  is  to  overcome  this  difficulty  that  the  author  has  prepared 
this  book  on  vocational  mathematics  for  girls.  He  does  not 
believe  in  omitting  the  regular  secondary  school  course  in 
mathematics,  but  offers  vocational  mathematics  as  an  introduc- 
tion to  the  regular  course. 

The  problems  have  been  used  by  the  author  during  the  past 
few  years  with  girls  of  high  school  age.  .  The  method  of  teach- 
ing has  consisted  in  arousing  an  interest  in  mathematics  by 
showing  its  value  in  daily  life.  Important  facts,  based  upon 
actual  experience  and  observation,  are  recalled  to  the  pupil's 
mind  before  she  attempts  to  solve  the  problems. 

A  discussion  of  each  division  of  the  subject  usually  precedes 
the  problems.  This  information  is  provided  for  the  regular 
teacher  in  mathematics  who  may  not  be  familiar  with  the 
subject  or  the  terms  used.  The  book  contains  samples  of 

iii 


A  1 


IV  PREFACE 

problems  from  all  occupations  that  women  are  likely  to  enter, 
from  the  textile  mill  to  the  home. 

The  author  has  received  valuable  suggestions  from  his  for- 
mer teachers  and  from  the  following :  Miss  Lilian  Baylies 
Green,  Editor  Ladies'  Home  Journal,  Philadelphia,  Pa. ;  Miss 
Bessie  Kingman,  Brockton  High  School,  Brockton,  Mass. ;  Mrs. 
Ellen  B.  McGowan,  Teachers  College,  New  York  City ;  Miss 
Susan  Watson,  Instructor  at  Peter  Bent  Brigham  Hospital, 
Boston ;  Mr.  Prank  F.  Murdock,  Principal  Normal  School, 
North  Adams,  Mass. ;  Mr.  Frank  Rollins,  Principal  Bushwick 
High  School,  Brooklyn ;  Mr.  George  M.  Lattimer,  Mechanics 
Institute,  Rochester,  N.  Y. ;  Mr.  J.  J.  Eaton,  Director  of  In- 
dustrial Arts,  Yonkers,  N.  Y. ;  Dr.  Mabel  Belt,  Baltimore,  Md. ; 
Mr.  Curtis  J.  Lewis,  Philadelphia,  Pa. ;  Mrs.  F.  H.  Consalus, 
Washington  Irving  High  School,  New  York  City ;  Miss  Griselda 
Ellis,  Girls'  Industrial  School,  Newark,  N.  J. ;  Mr.  J.  C.  Dono- 
hue,  Technical  High  School,  Syracuse,  N.  Y. ;  Mr.  W.  E.  Weaf er, 
Hutchinson-Central  High  School,  Buffalo,  N.  Y. ;  The  Bur- 
roughs Adding  Machine  Company  ;  The  Women's  Educational 
and  Industrial  Union ;  the  Department  of  Agriculture,  Wash- 
ington, D.  C. ;  and  Reports  of  Conference  of  New  York  State 
Vocational  Teachers. 

This  preface  would  not  be  complete  without  reference  to 
the  author's  wife,  Mrs.  Ellen  V.  Dooley,  who  has  offered  many 
valuable  suggestions  and  corrected  both  the  manuscript  and 
the  proof. 

The  author  will  be  pleased  to  receive  any  suggestions  or 
corrections  from  any  teacher. 


CONTENTS 

PART   I— REVIEW  OF   ARITHMETIC 

CHAPTER  PAGE 

I.     ESSENTIALS  OF  ARITHMETIC     .         ...         .         .         1 

Fundamental  Processes ;  Fractions ;  Decimals ;  Com- 
pound Numbers  ;  Percentage  ;  Ratio  and  Proportion  ; 
Involution  ;  Evolution. 

II.    MENSURATION     .        .        . 64 

Circles  ;  Triangles ;  Quadrilaterals  ;  Polygons ;  Ellipses ; 
Pyramid  ;  Cone  ;  Sphere  ;  Similar  Figures. 

III.  INTERPRETATION  OF  RESULTS  ......      80 

Reading  of  Blue  Print ;  Plans  of  a  Home ;  Drawing  to 
Scale ;  Estimating  Distances  and  Weight ;  Methods  of 
Solving  Examples. 

PART   II  — PROBLEMS   IN   HOMEMAKING 

IV.  THE  DISTRIBUTION  OF  INCOME 89 

Incomes  of  American  Families ;  Division  of  Income  ; 
Expense  Account  Book. 

V.     FOOD ,100 

Different  Kinds  of  Food  ;  Kitchen  Weights  and  Meas- 
ures ;  Cost  of  Meals  ;  Recipes  ;  Economical  Marketing. 

VI.     PROBLEMS  ON  THE  CONSTRUCTION  OF  A  HOUSE     .        .     128 

Advantages  of  Different  Types  of  Houses ;  Building 
Materials ;  Taxes  ;  United  States  Revenue. 

VII.     COST  OF  FURNISHING  A  HOUSE 146 

Different  Kinds  of  Furniture  ;  Hall ;  Floor  Coverings ; 
Linen  ;  Living  Room ;  Bedroom  ;  Dining  Room ;  Value 
of  Coal ;  How  to  Read  Gas  Meters  ;  How  to  Read  Elec- 
tric Meters  ;  Heating. 


VI  CONTENTS 

CHAPTER 

VIII.     THRIFT  AND  INVESTMENT 178 

Different  Institutions  of  Savings  ;  Bonds  ;  Stocks  ;  Ex- 
change ;  Insurance. 

PART   III  — DRESSMAKING  AND   MILLINERY 
IX.     PROBLEMS  IN  DRESSMAKING 198 

Fractions  of  a  Yard  ;  Tucks ;  Hem ;  Ruffles ;  Cost  of 
Finished  Garments  ;  Millinery  Problems. 

X.     CLOTHING .        .        .217 

Parts  of  Cloth  ;  Materials  of  Yarn ;  Kinds ;  Weight. 

PART  IV— THE   OFFICE   AND   THE   STORE 
XL     ARITHMETIC  FOR  OFFICE  ASSISTANTS   ....    233 
Rapid  Calculations  ;  Invoices ;  Profit  and  Loss  ;  Time 
Sheets  and  Pay  Rolls. 

XII.     ARITHMETIC  FOR  SALESGIRLS  AND  CASHIERS        .        .    260 
Saleslips  ;  Extensions  ;  Making  Change. 

XIII.  CIVIL  SERVICE 268 

PART   V  — ARITHMETIC   FOR  NURSES 

XIV.  ARITHMETIC  FOR  NURSES 276 

Apothecary's  Weights  and  Measures  ;  Household  Meas- 
ures ;  Approximate  Equivalents  of  Metric  and  English 
Weights  and  Measures ;  Doses ;  Strength  of  Solutions ; 
Prescription  Reading. 

PART  VI  — PROBLEMS   ON   THE   FARM 
XV.     PROBLEMS  ON  THE  FARM 304 

APPENDIX 317 

Metric  System ;  Graphs  ;  Formulas  ;  Useful  Mechanical 
Information. 

INDEX  365 


VOCATIONAL    MATHEMATICS 
FOR    GIRLS 

PART   I  — REVIEW  OF   ARITHMETIC 

CHAPTER   I 

Notation  and  Numeration 

A  unit  is  one  thing ;  as,  one  book,  one  pencil,  one  inch. 
A  number  is  made  up  of  units  and  tells  how  many  units  are 
taken. 

An  integer  is  a  whole  number. 

A  single  figure  expresses  a  certain  number  of  units  and  is  said  to  be  in 
the  units  column.  For  example,  5  or  8  is  a  single  figure  in  the  units 
column  ;  53  is  a  number  of  two  figures  and  has  the  figure  3  in  the  units 
column  and  the  figure  5  in  the  tens  column,  for  the  second  figure 
represents  a  certain  number  of  tens.  Each  column  has  its  own  name, 
as  shown  below. 


Sp3      00  r-       d 

•9s        ?    o        ~    *    "    m 

|  I  |  |  1  |  I  |  |  | 

JjlJjsJjJJjl 
138,  695,  4O   7,  125 

Reading  Numbers.  —  For  convenience  in  reading  and  writing 
numbers  they  are  separated  into  groups  of  three  figures  each 
by  commas,  beginning  at  the  right : 

138,695,407,125. 
The  first  group  is  125  units. 
The  second  group  is  407  thousands. 
The  third  group  is  695  millions. 
The  fourth  group  is  138  billions. 


2     A\K7^d<TION;A^.MA*fPSEMATICS  FOR  GIRLS 

The  preceding  number  is  read  one  hundred  thirty-eight 
billion,  six  hundred  ninety-five  million,  four  hundred  seven 
thousand,  one  hundred  twenty-five  ;  or  138  billion,  695  million, 
407  thousand,  125. 

Roman  Numerals 

A  knowledge  of  Roman  numerals  is  very  important.  Dates 
in  buildings  and  amounts  on  prescriptions  are  usually  expressed 
in  Roman  numerals.  They  are  also  used  for  numbering 
chapters  and  dials.  The  following  capital  letters,  seven  in 
all,  are  used  to  express  Roman  numerals  : 

IIIVXLCD  M 

One         Two         Five         Ten         Fifty  100  500  1000 

All  other  numbers  are  expressed  by  combining  the  letters 
according  to  the  following  principles : 

1.  When  a  letter  is  repeated,  the  value  is  repeated.     Thus, 
II  represents  2  ;  XXX,  30. 

2.  When  a  letter  of  less  value  is  placed  after  one  of  greater 
value,  the  lesser  is  added  to  the  greater.     Thus,  VII,  7  —  two 
added  to  five. 

3.  When  a  letter  of  less  value  is  placed  before  one  of  greater 
value,  the  lesser  is  taken  from  the  greater.     Thus,  IX,  9  —  ten 
less  one. 

Read  the  following  Roman  numerals  according  to  the  above 
rules : 


1. 

Ill 

9. 

XIX 

17. 

LXVI 

2. 

XXX 

10. 

LXXVII 

18. 

MDC 

3. 

ccc 

11. 

DCCCVII 

19. 

LXXII 

4. 

MMM 

12. 

XL 

20. 

CCLI 

5. 

VII 

13. 

XC 

21. 

DCLXVI 

6. 

LXXX 

14. 

IX 

22. 

DCXIV 

7. 

XXII 

15. 

XD 

23. 

MDXLVI 

8. 

XVIII 

16. 

XM 

24. 

MDCCXXIX 

REVIEW  OF  ARITHMETIC  3 

Express  the  following  numbers  in  Roman  numerals  : 

1.  14  4.    81  7.   281          10.    314          13.    1837 

2.  42  5.    73  8.   509         11.   573          14.   1789 

3.  69  6.   67  9.   812         12.   874         15.   80,003 

Standard  Mathematics  Sheet.  —  To  avoid  errors  in  solving  problems 
the  work  should  be  done  in  such  a  way  as  to  show  each  step  and  to  make 
it  easy  to  check  the  answer  when  found.  Paper  of  standard  size,  8£  in. 
by  11  in.,  should  be  used.  Rule  each  sheet  as  in  the  following  diagram, 
set  down  each  example  with  its  proper  number  in  the  margin,  and  clearly 
show  the  different  steps  required  for  the  solution.  To  show  that  the 
answer  obtained  is  correct,  the  proof  should  follow  the  example. 

STANDARD  MATHEMATICS  SHEET 


1. 

Mary  Smith  —  100 
Hp                  Vocational  Mathematics 
\                                              10-2-12    No.  10 

1,203                   2^ 
2,672                      2? 
31,118                     23 
480                      10 
39 
19,883 

'55,395     Ans. 

2. 

Proof: 

3. 

The  pupil  should  write  or  print  her  name  and  class,  the  date  when  the 
problem  is  finished,  and  the  number  of  the   problem   on  the   Standard 


4  VOCATIONAL  MATHEMATICS  FOR  GIRLS 

Mathematics  Sheet.  If  the  question  contains  several  divisions  or  prob- 
lems, they  should  be  tabulated — (a),  (/>),  etc.  —  at  the  left  of  the  prob- 
lems inside  the  margin  line.  A  line  should  be  drawn  between  problems 
to  separate  them. 

Addition 

Addition  is  the  process  of  finding  the  sum  of  two  or  more 
numbers.  The  result  obtained  by  this  process  is  called  the 
sum  or  amount. 

The  sign  of  addition  is  an  upright  cross,  +- ,  called  plus.  The 
sign  is  placed  between  the  two  numbers  to  be  added. 

Thus,  9  inches  +  7  inches  (read  nine  inches  plus  seven  inches). 

The  sign  of  equality  is  two  short  horizontal  parallel  lines,  = , 
and  means  equals  or  is  equal  to. 

Thus,  the  statement  that  8  feet  +  6  feet  =  14  feet,  means  that  six  feet 
added  to  eight  feet  (or  8  feet  plus  6  feet)  equals  fourteen  feet. 

To  find  the  sum  or  amount  of  two  or  more  numbers. 

EXAMPLE.  —  An  agent  for  a  flour  mill  sold  the  following  num- 
ber of  barrels  of  flour  during  the  day  :  1203,  2672,  31,118,  480, 
39,  and  19,883  bbl.  How  many  barrels  did  he  sell  during  the 

day? 

[The  abbreviation  for  barrels  is  bbl.] 

1,203  2$  The  sum  of  the  units  column  is  3  +  9  +  0 

2  672  20       4-8  +  2  +  3  =  25  units,  or  20  and  5  more  ; 

^1  1 1  k  9£      ^  ^s  tens,  so  leave  the   5  under  the  units 

"      column  and  add  the  2  tens  in  the  tens  column. 

*r      The  sum  of  the  tens  column  is  2  +  8  +  3+8 

39  +1+7  +  0  =  29  tens.     29  tens  equal  2  hun- 

19,883  dreds  and  9  tens.    Place  the  9  tens  under 

Sum  55,395  bbl.  the  tens  column   and   add  the  2   hundreds 

to  the  hundreds  column.     2+8  +  4  +  1+6 

+  2  =  23  hundreds  ;  23  hundreds  are  equal  to  2  thousands  and  3  hundreds. 
Place  the  3  hundreds  under  the  hundreds  column  and  add  the  2  thousands 
to  the  next  column.  2  +  9  +  1  +  2+  1  =  15  thousands,  or  1  ten-thousand 
and  5  thousands.  Add  the  1  ten-thousand  to  the  ten-thousands  column 


REVIEW  OF  ARITHMETIC  5 

and  the  sum  is  1  +  1  +  3  =  5.     Write  the  5  in  the  ten-thousands  column. 
Hence,  the  sum  is  55,395  bbl. 

TEST.  —  Repeat  the  process,  beginning  at  the  top  of  the  right-hand 
column. 

Exactness  is  very  important  in  arithmetic.  There  is  only 
one  correct  answer.  Therefore  it  is  necessary  to  be  accurate 
in  performing  the  numerical  calculations.  A  check  of  some 
kind  should  be  made  on  the  work.  The  simplest  check  is  to 
estimate  the  answer  before  solving  the  problem.  If  there  is 
a  great  discrepancy  between  the  estimated  answer  and  the 
answer  in  the  solution,  the  work  is  probably  wrong.  It  is 
also  necessary  to  be  exact  in  reading  the  problem. 

EXAMPLES 

1.  Write  the  following  numbers  as  figures  and  add  them  : 
Seventy-five  thousand  three  hundred  eight ;  seven  million  two 
hundred  five  thousand  eight  hundred  forty-nine. 

2.  In  a  certain  year  the  total  output  of   copper  from  the 
mines  was  worth  $  58,638,277.86.    Express  this  amount  in  words. 

3.  Solve  the  following  : 

386  +  5289  +  53666  +  3001  +  291  -f  38  =  ? 

4.  The  cost  of  the  Panama  Canal  was  estimated  in  1912  to 
be  $  375,000,000.     Express  this  amount  in  words. 

5.  A  farmer's  wife  received  the  following  number  of  eggs 
in  four  successive  weeks  :  692,  712,  684,  and  705  eggs.     How 
many  eggs  were  received  during  the  four  weeks  ? 

6.  A  woman  buys  a  two-family  house  for  $6511.00.     She 
makes  the   following   repairs :  mason-work,  $  112.00 ;   plumb- 
ing, $  146.00  ;  carpenter  work,  $  208.00  ;  painting  and  decora- 
ting, $  319.00.     How  much  does  the  house  cost  her  ? 

7.  Add  the  following  numbers,  left  to  right : 

a.  108,  219,  374,  876,  763,  489,  531,  681,  104 ; 

b.  3846,  5811,  6014,  8911,  7900,  3842,  5879. 


6          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

8.  According  to  the  census  of  1910  the  population  of  the 
United  States,  exclusive  of  the  outlying  possessions,  consisted 
of  47,332,277  males  and  44,639,989  females.     What  was  the 
total  population? 

9.  Wire  for  electric  lights  was  run  around  four  sides  of 
three  rooms.     If  the  first  room  was  13  ft.  long  and  9  ft.  wide ; 
the  second  18  ft.  long  and  18  ft.  wide;  and  the  third  12  ft. 
long  and   7  ft.  wide,  what  was  the  total  length  of   wire  re- 
quired?    Remember  that  electric  lights  require  two  wires. 

10.    Find  the  sum  : 

46  Ib.  +  135  Ib.  +  72  Ib.  +  39  Ib.  +  427  Ib.  +  64  Ib.  +  139  Ib. 

Subtraction 

Subtraction  is  the  process  of  finding  the  difference  between 
two  numbers,  or  of  finding  what  number  must  be  added  to  a 
given  number  to  equal  a  given  sum.  The  minuend  is  the  num- 
ber from  which  we  subtract ;  the  subtrahend  is  the  number 
subtracted ;  and  the  difference  or  remainder  is  the  result  of  the 
subtraction. 

The  sign  of  subtraction  is  a  short  horizontal  line,  — ,  called 
minus,  and  is  placed  before  the  number  to  be  subtracted. 

Thus,  12  —  8  =  4  is  read  twelve  minus  (or  less)  eight  equals  four. 

To  find  the  difference  of  two  numbers. 

EXAMPLE.  —  A  house  was  purchased  for  $  8074.00  twenty- 
five  years  ago.  It  was  recently  sold  at  auction  for  $  4869.00. 

What  was  the  loss  ? 

Write  the   smaller    number   under   the 

Minuend       $8074.00      greater,  with  units  of  the  same  order  in 
Subtrahend  $4869.00      the  same  vertical  line.    9  cannot  be  taken 

Remainder  $3205.00      from  4'  so  chan§e  l  *f  *°  unif  7Tbe  1 
ten  that  was    changed  from  the   7    tens 

makes  10  units,  which  added  to  the  4  units  makes  14  units.  Take  9 
from  the  14  units  and  5  units  remain.  Write  the  5  under  the  unit  col- 
umn. Since  1  ten  was  changed  from  7  tens,  there  are  6  tens  left,  and  6 
from  6  leaves  0.  Write  0  under  the  tens  column.  Next,  8  hundred  can- 


REVIEW   OF  ARITHMETIC  7 

not  be  taken  from  0  hundred,  so  1  thousand  (ten  hundred)  is  changed 
from  the  thousands  column.  8  hundred  from  10  hundred  leave  2  hun- 
dred. Write  the  2  under  the  hundreds  column.  Since  1  thousand  has 
been  taken  from  the  8  thousand,  there  are  left  7  thousand  to  subtract  the 
4  thousand  from,  which  leaves  3  thousand.  Write  3  under  the  thousand 
column.  The  whole  remainder  is  83205.00. 

PROOF.  —  If  the  sum  of  the  subtrahend  and  the  remainder  equals  the 
minuend,  the  answer  is  correct. 

EXAMPLES 

1.  Subtract  1001  from  79,999. 

2.  A  box  contained  one  gross  (144)  of  wood  screws.     If  48 
screws  were  used  on  a  job,  how  many  screws  were  left  in  the 
box? 

3.  What  number  must  be  added  to  3001  to  produce  a  sum 
of  98,322? 

4.  Barrels  are  usually  marked  with  the  gross  weight  and  tare 
(weight  of  empty  barrel).     If  a  barrel  of  sugar  is  marked  329 
Ib.  gross  weight  and  19  Ib.  tare,  find  the  net  weight  of  sugar. 

5.  A   box   contains  a  gross  (144)  of  pencils.     If  109  are 
removed,  how  many  remain? 

6.  A  farmer  received  1247  quarts  of  milk  in  October  and 
1189  quarts  in  November.     What  was  the  difference  ? 

7.  A  housewife  purchases  a  $  800.00  baby  grand  piano  for 
$  719.00.     How  much  does  she  save  ? 

8.  No.  1   cotton   yam   contains   840   yards  to  the  pound, 
while  No.  1  worsted  yarn  contains  560  yards  to  the  pound. 
What  is  the  difference  in  length? 

9.  A   young   lady  saved  $453.00  during  five  years.     She 
spent  $  189.00  on  a  sea  trip.     How  much  remained  ? 

10.  69,221  -  3008  =  ? 

11.  The  population  of  New  York  City  in  1900  was  3,437,202 
and  in  1910  was  4,766,883.     What  was  the  increase  from  1900 
to  1910? 


8  VOCATIONAL  MATHEMATICS  FOR   GIRLS 

12.  If  there  are  374,819  wage-earning  women  in  a  certain 
city  having  a  total  population  of  3,366,416  persons,  how  many  of 
the  residents  are  not  wage-earning  women  ? 

13.  In  the  year  1820  only  8385  immigrants  arrived  in  the 
United  States.    In  1842,  104,565  immigrants  arrived.     How 
many  more  arrived  in  1842  than  in  1820  ? 

14.  The  first  great  shoemaker  settled  in  Lynn,  Mass.,  in 
1636.     How  many  years  is  it  since  he  arrived  in  Lynn  ? 

Multiplication 

Multiplication  is  the  process  of  rinding  the  product  of  two 
numbers. 

Thus,  8x3  may  be  read  8  multiplied  by  3,  or  8  times  3,  and  means 
8  added  to  itself  3  times,  or  8  +  8  +  8  =  24  and  8x3  =  24. 

The  numbers  multiplied  together  are  called  factors.  The 
multiplicand  is  the  number  multiplied ;  the  multiplier  is  the 
number  multiplied  by ;  and  the  result  is  called  the  product. 

The  sign  of  multiplication  is  an  oblique  cross,  x ,  which 
means  multiplied  by  or  times. 

Thus,  7x4  may  be.  read  7  multiplied  by  4,  or  7  times  4. 

To  find  the  product  of  two  numbers. 

EXAMPLE.  —  A  certain  set  of  books  weighs  24  Ib.     What  is 

the  weight  of  17  sets  ? 

Write  the  multiplier  under  the  multipli- 

Mvltiplicand     24  Ib.       cand,  units  under  units,   tens  under  tens, 

Multiplier          17  etc.     7  times  4  units  equal  28  units,  which 

1(58  are  2  tens  and  8  units.     Place  the  8  under 

24  the  units  column.      The  2  tens  are  to  be 

p      ,  T7)«  11         added  to  the  tens  product.     7  times  2  tens 

are  14  tens  +  the  2  tens  are  16  tens,  or  1 

hundred  and  6  tens.  Place  the  6  tens  in  the  tens  column  and  the  1  hun- 
dred in  the  hundreds  column.  168  is  a  partial  product.  To  multiply  by 
the  1,  proceed  as  before,  but  as  1  is  a  ten,  write  the  first  number,  which 
is  4  of  this  partial  product,  under  the  tens  column,  and  the  next  number 
under  the  hundreds  column,  and  so  on.  Add  the  partial  products,  and 
their  sum  is  the  whole  product,  or  408  Ib. 


REVIEW  OF  ARITHMETIC  9 

EXAMPLES 

1.  A  milliner  ordered  58  spools  of  wire,  each  spool  contain- 
ing 100  yards.     How  many  yards  did  she  order  in  all  ? 

2.  Each  shoe  box  contains  12  pairs  of  shoes.     How  many 
pairs  in  423  boxes  ? 

3.  Multiply  839  by  291. 

4.  A  mechanic  sent  in  the  following  order   for   bolts :    12 
bolts,  6  Ib.  each;  9  bolts,  7  Ib.  each;  11  bolts,  3  Ib.  each;  6 
bolts,  2  Ib.  each;  and  20  bolts,  3  Ib.  each.     What  was  the 
total  weight  of  the  order  ? 

5.  Find  the  product  of  1683  and  809. 

To  multiply  by  10,  100,  1000,  etc.,  annex  as  many  ciphers  to 
the  multiplicand  as  there  are  ciphers  in  the  multiplier. 

EXAMPLE.  —  864  x  100  =  86,400. 

EXAMPLES 
Multiply  and  read  the  answers  to  the  following : 

1.  869  x  10  8.  100  x  500 

2.  1011  x  100  9.  1000  x  900 

3.  10,389  x  1000  10.  10,000  x  500 

4.  11,298  X  30,000          11.  10,000  x  6000 

5.  58,999  x  400  12.  1,000,000  x  6000 

6.  681,719  x  10  13.  1,891,717  x  400 

7.  801,369  x  100  14.  10,000,059  x  78,911 

Division 

Division  is  the  process  of  finding  how  many  times  one  num- 
ber is  contained  in  another.  The  dividend  is  the  number  to  be 
divided ;  the  divisor  is  the  number  by  which  the  dividend  is 
divided ;  the  quotient  is  the  result  of  the  division.  When  a 
number  is  not  contained  an  equal  number  of  times  in  another 
number,  what  is  left  over  is  called  a  remainder. 


10         VOCATIONAL  MATHEMATICS  FOR   GIRLS 

The  sign  of  division  is   -j-,  and  when  placed  between  two 
numbers  signifies  that  the  first  is  to  be  divided  by  the  second. 
Thus,  56  -s-  8  is  read  56  divided  by  8. 

Division  is  also  indicated  by  writing  the  dividend  above  the 
divisor  with  a  line  between. 

Thus,  5/  ;  this  is  read  56  divided  by  8. 

In  division  we  are  given  a  product  and  one  of  the  factors  to 
find  the  other  factor. 

To  find  how  many  times  one  number  is  contained  in  another. 

EXAMPLE.  —  A  manufacturer  desires  to  distribute  a  surplus 
of  $  8035.00  among  his  employees  so  that  each  one  will  re- 
ceive $  3.00  How  many  employees  will  receive  $  3.00  ?  How 

much  is  left  over  ? 

Write  the  numbers  in  the  manner 

2678  Employees      indicated  at  the  left.    8  thousand  is  in 
Divisor  3)8035  Dividend         the  thousands  column.    The  nearest  8 
g  thousand  can  be  divided  into  groups 

2Q  of  3  is  2  (thousand)  times,  which  gives 

.„  6  thousand.     Write    2    as    the    first 

figure  in  the  quotient  over  8  in  the 

dividend.      Place   the   6    (thousand) 

21  under  the  8  thousand  and  subtract ; 

25  the  remainder  is  2   thousand,  or  20 

24  hundred.     3  is  contained  in  20  hun- 

Remainder  ~T  dred  6  hundred  times,  or  18  hundred 

and  2  hundred  remainder.     Write  6 

as  the  next  figure  in  the  quotient.  Add  the  3  tens  in  the  dividend  to  the 
2  hundred,  or  20  tens,  and  23  tens  is  the  next  dividend  to  be  divided.  3  is 
contained  in  23  tens  7  times,  or  21  tens  with  a  remainder  of  2  tens.  Write 
7  as  the  next  figure  in  the  quotient.  2  tens,  or  20  units,  plus  the  5  units 
from  the  quotient  make  25  units.  3  is  contained  in  25,  8  times.  Write  8 
as  the  next  figure  in  the  quotient.  24  units  subtracted  from  25  units 
leave  a  remainder  of  1  unit.  Then  the  answer  is  2678  employees  and 
1  dollar  left  over. 

PROOF.  —  Find  the  product  of  the  divisor  and  quotient,  add  the  re- 
mainder, if  any,  and  if  the  sum  equals  the  dividend,  the  answer  is  correct. 


REVIEW  OF  ARITHMETIC  11 

EXAMPLES 

1.  A  strip  of  sheeting  measures  81"  in  width.     How  many 
pieces  6"  wide  can  be  cut  from  it?     Would  there  be  a  re- 
mainder ? 

2.  How  many  pieces   6"  long   can   be    cut  from  a  piece 
of  velvet   62"  long,   if   no   allowance   is    made   for  waste   in 
cutting  ? 

3.  If  the  cost  of  constructing  162  miles  of  railway  was 
$  4,561,200,  what  was  the  cost  per  mile  ? 

4.  If  a  job   which   took   379   hours  was  divided  equally 
among  25  women,  how  many  even  hours  would  each  woman 
work,  and  how  much  overtime  would  one  of  the  number  have 
to  put  in  to  complete  the  job? 

5.  The   "over-all"   dimension  on  a  drawing  was  18'  9". 
The  distance  was  to  be  spaced  off  into  14-inch  lengths,  begin- 
ning at  one  end.     How  many  such  lengths  could  be  spaced  ? 
How  many  inches  would  be  left  at  the  other  end  ? 

6.  If  a  locomotive  consumed  18  gallons  of  fuel  oil  per  mile 
of  freight   service,  how   far  could  it  run  with  2036  gallons 
of  oil? 

7.  If    6   eggs    weigh   one   pound,   how    many   cases   each 
containing  36  eggs  could  be  filled  from  a  stock  of  48  Ib.  of 
eggs? 

8.  The  American  people  spend  three  hundred  million  dollars 
every  year  on  shoes,  and  average  three  pairs  a  person.     What 
is  the  average  (wholesale)  cost  per  pair,  assuming  that  there 
are  91,972,266  people  in  the  United  States  ? 

9.  The  enlisted  strength  of  the  army  of  the  United  States 
in  1914  was  91,402  with  an  upkeep  charge  of  $  92,076,145.51. 
What  did  it  cost  the  United  States  per  man  to  maintain  its 
standing  army  that  year  ? 

10.  Divide  38,910  by  3896. 


12          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

REVIEW  EXAMPLES 

1.  A  farmer's  daughter  raised  on  the  farm  5  loads  of  pota- 
toes  containing  38   bu.,   29   bu.,  43  bu.,  39  bu.,  and  29  bu. 
respectively.     She  sold  12  bu.  to  each  of  three  families,  and 
34  bu.    to  each  of  four  families.     How  many  bushels  were 
left? 

2.  Five  pieces  of  cloth  are  placed  end  to  end.     If  each 
piece  contains  38  yards,  what  is  the  total  length  ? 

3.  I  bought  a  chair   for   $  3,  a  mat   for   $  1,  a  table  for 
$4,  and  gave  in  payment  a  $20  bill.     What  change  did  I 
receive  ? 

4.  A  teacupful  contains  4  fluid  ounces.     How  many  teacup- 
fuls  in  64  fluid  ounces  ? 

5.  No.  30  cotton  yarn  contains  25,200  yards  to  a  pound. 
How  many  pounds  of  yarn  in  630,000  yards  ? 

6.  The  consumption  of  water  in  a  city  during  the  month 
of  December   was   116,891,213   gallons   and   during   January 
115,819,729   gallons.     How   much   was   the   decrease   in   con- 
sumption ? 

7.  An  order   to   a   machine   shop   called   for   598   sewing 
machines  each  weighing  75  pounds.   What  was  the  total  weight  ? 

8.  If  a  strip  of  carpet  weighs  4  Ib.  per  foot  of  length,  find 
the  weight  of  one  measuring  16'  9"  in  length. 

9.  Multiply  641  and  225. 

10.  Divide  24,566  by  319. 

11.  An  order  was  given  for  ties  for  a  railroad  847  miles 
long.     If  each" mile  required  3017  ties,  how  many  ties  would  be 
needed  ? 

12.  How   many   gallons   of   milk   are  used   every    day  by 
two  hospitals,  if  one  uses  25  gallons  per  day  and  the  other  6 
gallons  less  ? 


REVIEW.  OF  ARITHMETIC  13 

Factors 

The  factors  of  a  number  are  the  integers  which  when  multi- 
plied together  produce  that  number. 

Thus,  21  is  the  product  of  3  and  7  ;  hence,  3  and  7  are  the  factors  of  21. 

Separating  a  number  into  its  factors  is  called  factoring. 

A  number  that  has  no  factors  but  itself  and  1  is  a  prime 
number. 

The  prime  numbers  up  to  25  are  2,  3,  5,  7,  11,  13,  17,  19  and  23. 

A  prime  number  used  as  a  factor  is  &  prime  factor. 

Thus,  3  and  5  are  prime  factors  of  15. 

Every  prime  number  except  2  and  5  ends  with  1,  3,  7,  or  9. 

To  find  the  prime  factors  of  a  number. 

EXAMPLE.  —  Find  the  prime  factors  of  84. 

2)84  The  prime  number  2  divides  84  evenly,  leaving  the  quotient 

2)42        ^'  which  2  divides  evenly.     The  next  quotient  is  21  which  3 
ov>^       divides,  giving  a  quotient  7.     7  divided  by  7  gives  the  last 
^—      quotient  1  which  is  indivisible.     The  several  divisors  are  the 
1L     prime  factors.     So  2,  2,  3,  and  7  are  the  prime  factors 
1      of  84. 
PROOF.  —  The  product  of  the  prime  factors  gives  the  number. 

EXAMPLES 
Find  the  prime  factors  : 

1.  63  4.  636          7.  1155 

2.  60  5.  1572         8.  7007 

3.  250  6.  2800          9.  13104 

Cancellation 

To  reject  a  factor  from  a  number  divides  the  number  by  that 
factor ;  to  reject  the  same  factors  from  both  dividend  and  divisor 
does  not  affect  the  quotient.  This  process  is  called  cancellation. 

This  method  can  be  used  to  advantage  in  many  everyday  cal- 
culations. 

EXAMPLE.  — Divide  12  x  18  x  30  by  6  x  9  x  4. 


14          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

1 

2        Jl       15  By  this  method  it  is  not 

Dividend  }$  X  J8  X  £0  necessary  to  multiply  be- 

Divisor         0X9X4     =3°  °UOft6n<'      foredividing-      locate 
lj      ^      '  the    division    by    writing 

the  divisor  under  the  divi- 
1  dend  with  a  line  between. 

Since  6  is  a  factor  of  6 

and  12,  and  9  of  9  and  18,  respectively,  they  may  be  cancelled  from  both 
divisor  and  dividend.  Since  2  in  the  dividend  is  a  factor  of  4  in  the 
divisor  it  may  be  cancelled  from  both,  leaving  2  in  the  divisor.  Then  the 
2  being  a  factor  of  30  in  the  dividend,  is  cancelled  from  both,  leaving  15. 
The  product  of  the  uncancelled  factors  is  30.  Therefore,  the  quotient 
is  30. 

PROOF.  —  If  the  product  of  the  divisor  and  the  quotient  equal  the 
dividend,  the  answer  is  correct. 


EXAMPLES 

Indicate  and  find  quotients  by  cancellation  : 

1.  Divide  36  x  27  x  49  x  38  x  50  by  70  x  18  x  15. 

2.  What  is  the  quotient  of  36  x  48  X  16  divided  by  27  x  24 
X8? 

3.  How  many  pounds  of  tea  at  50  cents  a  pound  must  be 
given  in  exchange   for   15   pounds  of  butter   at  40  cents   a 
pound  ? 

4.  There  are  16  ounces  in  a  pound  ;  30  pounds  of  steel  will 
produce  how  many  horseshoes,  if  each  weighs  6  ounces  ? 

5.  Divide  the  product  of  10,  75,  9,  and  96  by  the  product  of 
5,  12,  15,  and  9. 

6.  I  sold  16  dozen  eggs  at  30  cents  a  dozen  and  took  my 
pay  in  butter  at  40  cents  a  pound  :  how  many  pounds  did  I 
receive  ? 

7.  A  dealer  bought  16  cords  of  wood  at  $  4  a  cord  and  sold 
them  for  $  96  ;  find  the  gain  per  cord. 


REVIEW   OF  ARITHMETIC  15 


Greatest  Common  Divisor 

The  greatest  common  divisor  of  two  or  more  numbers  is  the 
greatest  number  that  will  exactly  divide  each  of  the  numbers. 

To  find  the  greatest  common  divisor  of  two  or  more  numbers. 

EXAMPLE.  —  Find  the  greatest  common  divisor  of  90  and 
150. 

90  =  2x3x5x3  2)90     150               First  Method 

150  =  2x3x5x5  5)45     75           The  prime  factors  com- 

Ans.  30  =  2  x  3  x  5  3)9     15     mon  to  both  90  aild  15° 

~Q       H      are  2,  3,  and  5.     Since 

2  x  3  x  5  =  30  Ans.  the  ^eatest  common  di~ 

visor  of  two  or  more  num- 

90)150(1  hers   is   the    product    of 

go  their  common  factors,  30 

7^\\QA/-i  is-  tne   greatest  common 

divisor  of  90  and  150. 
60 

Greatest  Common  Divisor  30)60(2  Second  Method 

gQ  To   find    the    greatest 

common     divisor     when 

the  numbers  cannot  be  readily  factored,  divide  the  larger  by  the  smaller, 
then  the  last  divisor  by  the  last  remainder  until  there  is  no  remainder. 
The  last  divisor  will  be  the  greatest  common  divisor.  If  the  greatest  com- 
mon divisor  is  to  be  found  of  more  than  two  numbers,  find  the  greatest 
common  divisor  of  two  of  them,  then  of  this  divisor  and  the  third  num- 
ber, and  so  on.  The  last  divisor  will  be  the  greatest  common  divisor  of 
all  of  them. 

EXAMPLES 

Find  the  greatest  common  divisor : 

1.  270,  810.  3.    504,  560.  5.   72,  153,  315,  2187. 

2.  264,312.          4.   288,432,1152. 

Least  Common  Multiple 

The  product  of  two  or  more  numbers  is  called  a  multiple  of 
each   of  them ;  4,  6,  8,  12  are  multiples   of  2.     The  common 


16          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

multiple  of  two  or  more  numbers  is  a  number  that  is  divisible 
by  each  of  the  numbers  without  a  remainder ;  60  is  a  common 
multiple  of  4,  5,  6. 

The  least  common  multiple  of  two  or  more  numbers  is  the 
smallest  common  multiple  of  the  number;  30  is  the  least 
common  multiple  of  3,  5,  6. 

To  find  the  least  common  multiple  of  two  or  more  numbers. 
EXAMPLE.  —  Find   the   least   common   multiple   of  21,   28, 

First  Method 

21  =  3  X  7  Take  all  the  factors  of  the  first  number,  all  of 

28  =  2  X  2  X  J      the  second  not  already  represented  in  the  first,  etc. 

30  =  2  X  £  X  5      Tnus> 

3  x  7  x  2  x  2  x  5  =  420  L.  C.  M. 

Second  Method 

2)21     28     30 

3)21     14     15 

7)7     14       5 

125 

2  x  3  x  7  x  1  X  2  x  5  =  420  L.  C.  M. 

Divide  any  two  or  more  numbers  by  a  prime  factor  contained  in  them, 
like  2  in  28  and  30.  Write  21  which  is  not  divided  by  the  2  for  the  next 
quotient  together  with  the  14  and  15.  3  is  a  prime  factor  of  21  and  15 
which  gives  a  quotient  of  7  and  5  with  14  written  in  the  quotient  undi- 
vided. 7  is  a  prime  factor  of  7  and  14  which  gives  a  remainder  of  1,  2  ; 
and  5  undivided  is  written  down  as  before.  The  product  420  of  all  these 
divisors  and  the  last  quotients  is  the  least  common  multiple  of  21,  28, 
and  30. 

EXAMPLES 

Find  the  least  common  multiple : 

1.   18,  27,  30.         2.   15,  60,  140,  210.          3.   24,  42,  54,  360. 
4.   25,20,35,40.  5.   24,48,96,192. 

6.  What  is  the  shortest  length  of  rope  that  can  be  cut  into 
pieces  32',  36',  and  44'  long? 


REVIEW   OF  ARITHMETIC  17 

Fractions 

A  fraction  is  one  or  more  equal  parts  of  a  unit.  If  an  apple 
be  divided  into  two  equal  parts,  each  part  is  one-half  of  the 
apple,  and  is  expressed  by  placing  the  number  1  above  the 
number  2  with  a  short  line  between :  |-.  A  fraction  always 
indicates  division.  In  1,  1  is  the  dividend  and  2  the  divisor ; 
1  is  called  the  numerator  and  2  is  called  the  denominator. 

A  common  fraction  is  one  which  is  expressed  by  a  numerator 
written  above  a  line  and  a  denominator  below.  The  nu- 
merator and  denominator  are  called  the  terms  of  the  fraction. 

A  proper  fraction  is  a  fraction  whose  value  is  less  than  1 ;  its 
numerator  is  less  than  its  denominator,  as  f,  £,  f,  |^-.  An 
improper  fraction  is  a  fraction  whose  value  is  1  or  more  than  1; 
its  numerator  is  equal  to  or  greater  than  its  denominator,  as  f, 
-}-§-.  A  number  made  up  of  an  integer  and  a  fraction  is  a 
mixed  number.  Read  with  the  word  and  between  the  whole 
number  and  the  fraction :  4T9g-,  3-J-,  etc. 

The  value  of  a  fraction  is  the  quotient  of  the  numerator 
divided  by  the  denominator.  • 

EXERCISE 

Read  the  following : 

1.  f  3.    121  5.   51  7.   9^  9.   J 

2.  «          4.   81  6.    6J  8.   12A 

Reduction  of  Fractions 

Reduction  of  fractions  is  the  process  of  changing  their  form 
without  changing  their  value. 

To  reduce  a  fraction  to  higher  terms. 

Multiplying  the  denominator  and  the  numerator  of  the  given 
fraction  by  the  same  number  does  not  change  the  value  of  the 
fraction. 


18          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

EXAMPLE.  —  Reduce  •§  to  thirty-seconds. 

The  denominator  must  be  multiplied  by  4  to 

_  X  _  —  _    Ans.      obtain  32  ;  so  the  numerator  must  be  multiplied 
8      4       32  by  the  same  number  in  order  that  the  value  of 

the  fraction  may  not  be  changed. 

EXAMPLES 

Change  the  following : 

1.  |  to  27ths.  6.  /-j  to  75ths. 

2.  -i-l  to  60ths.  7.  £§-  to  144ths. 

3.  I  to  40ths.  8.  fj  to  168ths. 

4.  |  to  56ths.  9.  ||  to  522ds. 

5.  T9Q  to  50ths.  10.  £ff  to  9375ths. 

A  fraction  is  said  to  be  in  its  lowest  terms  when  the  numera- 
tor and  the  denominator  are  prime  to  each  other. 

To  reduce  a  fraction  to  its  lowest  terms. 

Dividing  the  numerator  and  the  denominator  of  a  fraction 
by  the  same  number  does  not  change  the  value  of  the  fraction. 
The  process  of  dividing  the  numerator  and  denominator  of  a 
fraction  by  a  number  common  to  both  may  be  continued  until 
the  terms  are  prime  to  each  other. 

EXAMPLE.  —  Reduce  |-|  to  fourths. 

The  denominator  must  be  divided  by  4  to  give 

12 3     j  the  new  denominator  4  ;  then  the  numerator  must  be 

16      4  divided  by  the  same  number  so  as  not  to  change  the 

value  of  the  fraction. 

If  the  terms  of  a  fraction  are  large  numbers,  find  their 
greatest  common  divisor  and  divide  both  terms  by  that. 

EXAMPLE.  —  Reduce  f  £f£  to  fourths. 

(1)          2166)2888(1  (2)  2166  =  3     , 

2166  2888     4  " 

G.  C.  D.       722)2166(3 
2166 


REVIEW   OF  ARITHMETIC  19 

EXAMPLES 

Reduce  to  lowest  terms  : 

1-  A  3-    Ml  5-    H  7-    W  9-    ttt 

2-  »»  4-    it  6.    TW  8.    HI  10. 

To  reduce  an  integer  to  an  improper  fraction. 
EXAMPLE.  —  Reduce  25  to  fifths. 

25  times  |  =  if*   Ans.       ,   *"  l  t5 

25  times  f  ,  or  if  £. 

To  reduce  a  mixed  number  to  an  improper  fraction. 
EXAMPLE.  —  Reduce  16^  to  an  improper  fraction. 


_  I  sevenths  Since  jn  j  there  are  ^  in  16  there  must 

112  be  16  times  £,  or  i|a. 

__4  sevenths  H^  +  I  =  1**- 

116  sevenths,  =  1^. 

EXAMPLES 
Reduce  to  improper  fractions  : 

1.  3£  3.   17J  5.   13J-  7.   359T% 

2.  16&  4.   121  6.   27^  8.   482i| 
9.   25^                                     10.   Reduce  250  to  16ths. 

11.  Change  156  to  a  fraction  whose  denominator  shall  be  12. 

12.  In  $  730  how  many  fourths  of  a  dollar  ? 

13.  Change  12f  to  16ths.          14.    Change  24|  to  18ths. 

To  reduce  an  improper  fraction  to  an  integer  or  mixed  number 
divide  the  numerator  by  the  denominator. 

EXAMPLE:  —  Reduce  -3T8g-5-  to  an  integer  or  mixed  number. 
24 

16)385 

^2  Smce  T!  e(lual  1*  ¥<r  wil1  eQual  as  many 

—  —  times  1  as  16  is  contained  in  385,  or  24^ 

bo  Z4:^Q    Ans.      timeSt 

64 
1 


20          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

EXAMPLES 

Reduce  to  integers  or  mixed  numbers : 

1-     tt  *     Aff±  7.      8J)f  1Q. 

2.  \v9-  5-  -3¥<r6JL  8-  W  11- 

3.  *«*  6.  A™  9.  aflftn  12.  || 

When  fractions  have  the  same  denominator  their  denomi- 
nator is  called  a  common  denominator. 
Thus,  |f,  T%,  y's  have  a  common  denominator. 

The  smallest  common  denominator  of  two  or  more  fractions  is 
their  least  common  denominator. 

Thus,  |§,  T\,  T2s  become  f,  f ,  £  when  changed  to  their  least  common 
denominator. 

The  common  denominator  of  two  or  more  fractions  is  a 
common  multiple  of  their  denominators. 

The  least  common  denominator  of  two  or  more  fractions  is 
the  least  common  multiple  of  their  denominators. 

EXAMPLE.  — Reduce  f  and  f  to  fractions  having  a  common 
denominator. 

3.  x  6.  _  i_8.  The   common    denominator  must  be   a 

*       4  _  2  o  common  multiple   of  the   denominators  4 

=  ^  20          and  6'  and  Since  24  is  the  Product  of  the 

¥  ==  1TT  anc*-  ¥  =  "2T          denominators,  it  is  a  common  multiple  of 

them.     Therefore,  24  is  a  common  denominator  of  f  and  f . 

To  reduce  fractions  to  fractions  having  the  least  common  denominator. 

EXAMPLE.  —  Reduce  -|,  ^,  and  -£%  to  fractions  having  the 
least  common  denominator. 

2">  S     6     12  ^e  least  common  de* 

* nominator    must    be    the 

^)^     ^        ^  least  common  multiple  of 

112  the  denominators  3,  6,  12, 

2  x  3  x  2  =  12   L.C.M.  which  is  12. 

I  =  J^. ;    I  =  |f .    _?_  _  _L.     ^ws<  Divide  the  least  common 

multiple  12  by  the  denom- 
inator of  each  fraction,  and  multiply  both  terms  by  the  quotient.     If  the 


REVIEW   OF  ARITHMETIC  21 

denominators  should  be  prime  to  each  other,  their  product  would  be  their 
least  common  denominator. 

EXAMPLES 

Reduce  to  fractions  having  a  common  denominator  : 

I-    i,  f  5.    f  ,  f  ,  f 

2     |,|  6.    |,  f,|- 

3.    f  ,  i  7.    1   f  ,  f,  f 

4-    f  T4>  *  8-    i>  A.  *,  i 

Reduce  to  fractions  having  least  common  denominator: 

1-  t,  1,  -h  *    *,  f  >  A,  4 

2-  i  i  A  6.    f  ,  f  ,  J,  | 

3-  AJ  2T>  f  7.   Which  fraction  is  larger, 


Addition  of  Fractions 

Only  fractions  with  a  common  denominator  can  be  added. 
If  the  fractions  have  not  the  same  denominator,  reduce  them 
to  a  common  denominator,  add  their  numerators,  and  place 
their  sum  over  the  common  denominator.  The  result  should  be 
reduced  to  its  lowest  terms.  If  the  result  is  an  improper 
fraction,  it  should  be  reduced  to  an  integer  or  mixed  number. 

EXAMPLE.  —  Add  J,  ^,  and  T9g. 

a     ^a  The        least 

1.    2)4     6     16  common  multi- 

2)2     3       8  pie  of  the  de- 

13       4     48  L.  C.  M.  nominators     is 


nominator  of  each  fraction  and  multiplying  both  terms  by  the  quotient 
give  ff,  |f,  ||  .  The  fractions  are  now  like  fractions,  and  are  added  by 
adding  their  numerators  and  placing  the  sum  over  the  common  denomi- 
nator. Hence,  the  sum  is  -W/-,  or  2?7^. 


22          VOCATIONAL  MATHEMATICS  FOR  GIRLS 

EXAMPLE.  —  Add  5f ,  7T^,  and  6T7^. 

First   find   the  sum   of   the  fractions, 

which   is  f§>   or  iff-     Add  this  to  the 
sum   of  the    integers,    18.      18  +  If  §  = 

=  19|f .     ^4rcs.     19M- 

EXAMPLES 

1.  Find   the   "  over-all "   dimension    of    a   drawing   if   the 
separate  parts  measure  T%",  f ",  |",  and  f",  respectively. 

2.  Find  the  sum  of  |,  },  -J-,  |£,  and  f  1. 

3.  Find  the  sum  of  3f ,  4f ,  and  2TV 

4.  A  seam  T3g  of  an  inch  wide  is  made  on  both  sides  of  a 
piece  of  cloth  27  inches  wide.     What  is  the  width  after  the 
seams  are  made  ? 

5.  I  bought  cotton  cloth  valued  at  $  6  J,  silk  at  $  13J,  hand- 
kerchiefs for  $2J,  and  hose  for  $2J.     What  was  the  whole 
cost? 

6.  A  ribbon  was  cut  into  two  pieces,  one  8f"  and  the  other 
5-fa"  long.     If  Jg-"  was  allowed  for  waste  in  cutting,  what  was 
the  length  of  the  ribbon  ? 

7.  Three  pieces  of  cloth  contain  38^,  12-J-,  and  53|-  yards  re- 
spectively.    What  is  their  total  length  in  yards  ? 

8.  Add:  101  7f  11,  if. 

9.  Add  :  1361,  184 j,  416J,  125|. 

Subtraction  of  Fractions 

Only  fractions  with  a  common  denominator  can  be  sub- 
tracted. If  the  fractions  have  not  the  same  denominator, 
reduce  them  to  a  common  denominator  and  write  the  differ- 
ence of  their  numerators  over  the  common  denominator.  The 
result  should  be  reduced  to  its  lowest  terms. 


REVIEW   OF  ARITHMETIC  23 

EXAMPLE.  —  Subtract  f  from  J. 

The  least  common  denominator  of  f 

5  _  I  =  |  _  |-  =  J.     Ans.      and  f  is  6.     f  =  f ,  and  f  =  f .     Their 

difference  is  £. 

EXAMPLE.  —  From  11|  subtract  5f . 

•MI  _  jQ_g  When    the    fractions    are    changed   to 

®  their  least  common  denominator,  they  are 

4B~  ==    4TT  n|  _  45 _     s  cannot  be  subtracted  from  f, 

6f  =  6J-     ^ns-       hence  1  is  taken  from  11  units,  changed  to 

sixths,  and  added  to  the  f,  which  makes  f .     lOf  —  4|  =  6|  =  6^. 

EXAMPLES 

1.  From  eleven  yards  of  cloth,  If  yards  were  cut  for  a 
jacket  and  3J  yards  for  a  coat.     How  many  yards  were  left  ? 

2.  From  a  firkin  of  butter  containing  271  lb.  there  were 
sold  3|  lb.  and  11^  lb.     How  many  pounds  remained? 

3.  The  sum  of  two  fractions  is  f .     One  of  the  fractions  is 
^.     Find  the  other. 

4.  Laura  had  $  1\  and  gave  away  $  2^  and  $  3J.     How 
much  remained  ? 

5.  The  sum  of  2  numbers  is  371  and  one  of  the  numbers  is 
28f .     Find  the  other  number. 

o 

6.  By  selling  goods  for  $  431,  I  lost  $  271.     What  was  the 
cost? 

7.  A  man  sells  9|  yards  from  a  piece  of  cloth  containing 
34  yds.     How  many  yards  remain  ? 

8.  Mr.  Brown  sold  goods  for  $  56y3¥,  gaining  $  12.     What 
did  they  cost  ? 

9.  A  dealer  had  208  tons  of  coal  and  sold  92|  tons.     How 
much  remained  ? 

10.    If  I  buy  a  ton  of  coal  for  $  6J  and  sell  for  $  71,  how 
much  do  I  gain  ? 


24          VOCATIONAL  MATHEMATICS  FOR  GIRLS 

14.  There  were  48  J  gallons  in  the  tank.     First  41  gallons 
were  used,  then  5^  gallons,  and  last  2f  gallons.     How  many 
gallons  were  left  in  the  tank  ? 

15.  What  is  the  difference  between  T9T  and  if  ? 

16.  What  is  the  difference  between  32  J  and  3£J  ? 

17.  A  piece  of  dress  goods  contains  60  yd.     If   four  cuts 
of   12  L,  9 1,  18f,  and   101  yd.    respectively   are  made,   what 
remains  ? 

Multiplication  of  Fractions 

To  multiply  fractions,  multiply  the  numerators  together  for  the 
neiv  numerator  and  multiply  the  denominators  together  for  the 
new  denominator. 

Cancel  when  possible.  The  word  of  between  two  fractions 
is  equivalent  to  the  sign  of  multiplication. 

To  multiply  a  mixed  number  by  an  integer,  multiply  the  whole 
number  and  the  fraction  separately  by  the  integer  then  add  the 
products. 

To  multiply  two  mixed  numbers,  change  each  to  an  improper 
fraction  and  multiply. 

EXAMPLE.  —  Multiply  |  by  f . 

\  multiplied  by  f  is  the  same  as  |  of  f .  3  and  5  are  prime  to  each  other 
so  that  answer  is  f .  This  method  of  solution  is  the  same  as  multiplying 
the  numerators  together  for  a  new  numerator  and  the  denominators  for 
a  new  denominator.  Cancellation  shortens  the  process. 

EXAMPLE. — Find  the  product  of  124  J  and  5. 

124f 

~  If  the  fraction  and  integer  are  mul- 

~^T  *  v  s  _  is  _  QS       tiplied  separately  by  5,  the  result  is  5 

6t  ?       times  f  =  -V  =  3f,  and  5  times  124  = 

620  620.     620  +  3f  =623f . 

623f  Ans. 


REVIEW  OF  ARITHMETIC  25 

EXAMPLES 

1.  William  earns  831  cents  a  day.      How  much  will  he 
earn  in  five  weeks  ? 

2.  One  bag  of  flour  costs  75  cents.     How  much  will  three 
barrels  cost  ?     A  barrel  holds  8  bags. 

3.  From  a  barrel  of  flour  containing  196  lb.,  241-  lb.  were 
taken.     At  another  time  \  of  the  remainder  was  taken.     How 
many  pounds  were  left  ? 

4.  Multiply  J  of  f  by  f  of  f  . 

5.  Multiply  26f  by  91. 

6.  Find  the  cost  of  19|  yd.  of  cloth  at  161  cents  a  yard. 

7.  At  $  121   each,  how   many  tables   can  be   bought   for 
$280? 

8.  I  paid  $  6  1  for  a  barrel  of  flour  and  sold  it  for  $  T97  more. 
How  much  did  I  sell  it  for  ? 

9.  What  is  the  cost  of  18  yards  of  cloth  at  15J  cents  a  yard  ? 

10.  If  coal  cost  $7-J-  a  ton,  how  much  will  8J  tons  cost  ? 

11.  Multiply  :  32|  by  8  j. 

Division  of  Fractions 

To  divide  one  fraction  by  another,  invert  the  divisor  and 
proceed  as  in  multiplication  of  fractions.  Change  integers  and 
mixed  numbers  to  improper  fractions. 

EXAMPLE.  —  Divide  f  x  f  by  f  x  f  . 


A      3       /?       H      3  The  divisor  f  x  f  is  inverted  and  the 

^X-X^X^  =  -.  Ans.     result  obtained  by  the  process  of  cancel- 
5  0      ?>      5  lation. 


26          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

EXAMPLE.  —  Divide  3156f  by  5. 
Ans. 


*  When  the  integer  of  a  mixed 

30  number    is    large,    it    may    be 

15  divided  as  follows  :  5  in  3156f  , 

15  1  J  =  |-                              631  times,  with  a  remainder  of 

(^  If.     This  remainder  divided  by 

K  6  gives  270,  which  is  placed  at 

K  the  right  of  the  quotient. 

If 


EXAMPLE.  —  Divide  3682  by  5J. 

When  the  dividend  is  a  large  number  and 

5 1)  3682  the  divisor  a  mixed  number,  it  is  useful  to  re- 

2  2  member  that  multiplying  both  dividend  and  di- 

TT  \-oflyi  '  visor  by  the  same  number  does  not  change  the 

quotient.     In  this  example   we  can  multiply 

boy Yj    Ans.      footh  dividend  and  divisor  by  2  and  then  divide 

as  with  whole  numbers.     The  quotient  is  669T5T. 

A  fraction  having  a  fraction  for  one  or  both  of  its  terms  is 
called  a  complex  fraction. 

To  reduce  a  complex  fraction  to  a  simple  fraction. 
EXAMPLE.  —  Reduce  _I  to  a  simple  fraction. 

6 


Change  4f  and  7f  to  improper  fractions,  J/  and  4/,  respectively.  Per- 
form the  division  indicated  with  the  aid  of  cancellation  and  the  result  will 
be  |f. 

EXAMPLES 

1.  Divide^  by  f  7.   296-=-10i  =  ? 

2.  Divide  TV  by  f.  8.   28,769  ^7|=? 

3.  Divide  |f  by  i.  7i_? 

4.  Divide  $  by  \.  '   ft 

5.  Dividef  by  f.  iofi 


6.   384|  --  5  =  ?  1  X 


REVIEW   OF  ARITHMETIC  27 

REVIEW  PROBLEMS   IN   FRACTIONS 

1.  Two  and  one  half  yards  of  cloth  cost  $  2.75.     What  is 
the  price  per  yard  ? 

2.  An  8i-qt.  can  of  milk  is  bought  from  a  farmer  for. 60 
cents.     What  is  the  cost  per  quart  ? 

3.  I  paid  56  cents  for  f  of  a  yard  of  lace.     What  was  the 
price  per  yard  ? 

4.  A  farmer's  daughter  sold  a  weekly  supply  of  eggs  for 
$  5.70.     If  she  received  28^  cents  a  dozen,  how  many  dozen 
did  she  sell  ? 

5.  If  a  narrow  piece  of  goods,  6J  yd.  long,  is  cut  into  pieces 
6}  inches  long,  how  many  pieces  can  be  cut?     How  much 
remains  ?     Allow  -J-  in.  for  waste. 

6.  What  is  the  cost  of  18^  pounds  of  crackers  at  17^  cents 
a  pound  ? 

7.  A  gallon  (U.  S.  Standard  capacity)  contains  231  cubic 

inches. 

a.  Give  number  of  cubic  inches  in  J  gallon. 

b.  Give  number  of  cubic  inches  in  1  quart. 

c.  Give  number  of  cubic  inches  in  1  pint. 

d.  Give  number  of  cubic  inches  in  1  pint. 

8.  A  woman  earns  $  2%  a  day.     If  she  spends  $  If,  how 
much  does   she   save  ?     How  many  weeks   (six  full  working 
days)  will  it  take  to  save  $  90  ? 

9.  I  paid  56  cents  for  f  of  a  yard  of  lace.     What  was  the 
price  per  yard  ? 

10.  A  furniture  dealer  sold  a  table  for  $  141,  a  couch  for 
$  45f ,  a  desk  for  $  llf ,  and  some  chairs  for  $  27T%.     Find  the 
amount  of  his  sales. 

11.  A  woman  had  $  200.     She  lost  £  of  it,  gave  away  J  the 
remainder,  and  spent  $  20J.     How  much  had  she  left  ? 

12.  I  gave  $  16J  for  33  yards  of  cloth.     How  much  did  one 
yard  cost  ? 


28          VOCATIONAL  MATHEMATICS  FOR  GIRLS 


REVIEW  OF  ARITHMETIC  29 


22. 

i 

-A 

_  9 

33. 

f  - 

i  = 

9 

44. 

i 

"A 

__  9 

23. 

i 

-A 

__  9 

34. 

t 

A  = 

9 

45. 

| 

-A 

=  ? 

24. 

i 

-A 

_  9 

35. 

t 

1     . 
3T  - 

9 

46. 

•H- 

-  A 

=  ? 

25. 

i 

-A 

__  9 

36. 

t  - 

A  = 

? 

47. 

T2 

-  A 

_  9 

26. 

& 

-A 

_  9 

37. 

tt- 

A  = 

9 

48. 

A 

-A 

_  9 

27. 

T¥S 

-A 

_  9 

38. 

i  - 

sV  = 

9 

49. 

I 

-i 

_  9 

28. 

A 

.  JL 
1  6 

_  9 

39. 

ti- 

A  = 

9 

50. 

I 

-i 

_  9 

29. 

A 

-A 

_  9 

40. 

H- 

A  = 

9 

51. 

i 

"~    8" 

_  9 

30. 

A 

-  A 

r> 

41. 

A- 

T2    = 

9 

52. 

i 

-TV 

=  ? 

31. 

i 

i 

~  "2 

=   ? 

42. 

it- 

A  = 

'? 

53. 

1 

-1T2 

=  ? 

32. 

f 

-i 

_  9 

43. 

i  - 

if  = 

=  ? 

54. 

i 

-A 

_  9 

Multiplication 

1. 

ix 

1  = 

9 

19. 

i   x 

2-      = 

9 

37. 

A 

xi 

_  9 

2. 

ix 

1       

9 

20. 

t   x 

i      = 

9 

38. 

A 

xi 

=  9 

3. 

ix 

1 

8      ' 

9 

21. 

i    x 

i      = 

9 

39. 

A 

xi 

=  9 

4. 

ix 

T6   = 

9 

22. 

1              vx 

1     _ 

1  6 

9 

40. 

A 

xA 

=  9 

5. 

ix 

A  = 

9 

23. 

i   x 

sV  = 

9 

41. 

A 

x  A 

_  9 

6. 

ix 

A  = 

9 

24, 

i    x 

A  = 

9 

42. 

A 

x  A 

_  9 

7. 

ix 

i   = 

9 

25. 

A  x 

i    = 

9 

43. 

A 

xi 

=  9 

8. 

ix 

i  = 

9 

26. 

AX 

i    = 

9 

44. 

A 

xi 

_  9 

9. 

ix 

i  = 

9 

27. 

AX 

i    

9 

45. 

6V 

xi 

=  9 

10. 

ix 

A  = 

9 

28. 

AX 

A  = 

9 

46. 

6\ 

xA 

_  9 

11. 

ix 

A  = 

9 

29. 

AX 

A  = 

9 

47. 

A' 

x  A 

=  9 

12. 

ix 

A  = 

9 

30. 

AX 

i  

6  4 

9 

48. 

A 

xA 

_  9 

13. 

fx 

i   = 

9 

31. 

3       v 
4       X 

i  = 

9 

49. 

I 

xi 

=  9 

14. 

—  X 

4      = 

9 

32. 

3        V 
4       A 

i  = 

9 

50. 

J 

xi 

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15. 

f  x 

1       

8 

9 

33. 

3       x 

i  = 

9 

51. 

i 

xi 

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16. 

fx 

A  = 

9 

34. 

f    x 

A  = 

9 

52. 

1 

xA 

_  9 

17. 

f  x 

A  = 

9 

35. 

3        V 
4       A 

A  = 

9 

53. 

1 

x  A 

=  ? 

18. 

f  x 

A  = 

9 

36. 

f   x 

\   

Q 

54. 

f 

x  A 

_  9 

30          VOCATIONAL  MATHEMATICS  FOR   GIRLS 


Division 

1. 

i-*-i 

_  9 

19. 

i 

"^  \ 

—  9 

37. 

3T 

-5-J     =? 

2. 

i   .  i 

"2"  ~  ¥ 

_  9 

20. 

i 

+4 

=  9 

38. 

3V 

.     i      o 

3. 

i  +  i 

_  9 

21. 

i 

+  4 

9 

39. 

A 

-7-    1          =    ? 

4. 

I^-T6 

_  9 

22. 

i 

8" 

^-y1^ 

.  —  9 

40. 

A 

•*•  T6  =  ? 

5. 

i-s-A 

=  9 

23. 

i 

"^A 

.  =  9 

41. 

aV 

^A=? 

6. 

i^-6¥ 

9 

24. 

i 

-r-  ^ 

.=  9 

42. 

sV 

-t.   1    =  ? 

7. 

1    .    1 

¥  ~  2 

_  9 

25. 

T6 

.     1 
~  2" 

_  9 

43. 

A 

H-J    -? 

8. 

1     .     1 
¥    '    ¥ 

=  9 

26. 

T6 

+4 

_  9 

44. 

A 

-^-i     =? 

9. 

i-*-i 

_  9 

27. 

A 

-i 

_  9 

45. 

A 

_:_  1     _  9 

10. 

4  +  A 

_  9 

28. 

T6 

-5-  T\ 

r—  9 

46. 

-h 

-«-  T  6  =  ? 

11. 

i-i-A 

—  9 

29. 

TV 

-i-  g\ 

,  =  ? 

47. 

A 

•••  -fa  =  ? 

12. 

i-^s-V 

=  9 

30. 

iV 

-*-A 

.  =  9 

48. 

6T 

•*•  A  =  ? 

13. 

4  +  i 

_  9 

31. 

8 

¥ 

.    1 

~  2" 

_  9 

49. 

1 

-v-1     =? 

14. 

4  -"4 

=  ? 

32. 

I 

_._  1 

=  9 

50. 

1 

^-¥     =? 

15. 

4  +  4 

=  9 

33. 

3 
4 

+  t 

_  9 

51. 

1 

+  i     =? 

16. 

i-iV 

_  9 

34. 

8 

¥ 

^-Tl 

r=? 

52. 

i 

-J-iV  =  ? 

17. 

•5  _:_  _1_ 

_  9 

35. 

f 

^-^ 

.  _  9 

53. 

J 

^A=? 

18. 

"8  ~*~~6¥ 

=  9 

36. 

i 

-7-g-1^ 

.=  9 

54. 

1 

•*-  6¥  =  ? 

Decimal  Fractions 

A  power  is  the  product  of  equal  factors,  as  10  x  10  =  100. 
10  x  10  x  10  =  1000.  100  is  the  second  power  of  10.  1000  is 
the  third  power  of  10. 

A  decimal  fraction  or  decimal  is  a  fraction  whose  denominator- 
is  10  or  a  power  of  10.  A  common  fraction  may  have  any 
number  for  its  denominator,  but  a  decimal  fraction  must  always 
have  for  its  denominator  10,  or  a  power  of  10.  A  decimal  is 
written  at  the  right  of  a  period  (.),  called  the  decimal  point. 
A  figure  at  the  right  of  a  decimal  point  is  called  a  decimal 
figure. 

^  =  .5  ;  TVo  =  -25 ;  T^  =  .07  ;  T^  =  .016. 


REVIEW  OF  ARITHMETIC  31 

A  mixed  decimal  is  an  integer  and  a  decimal ;  as,  16.04. 

To  read  a  decimal,  read  the  decimal  as  an  integer,  and  give 
it  the  denomination  of  the  right-hand  figure.  To  write,  a  deci- 
mal, write  the  numerator,  prefixing  ciphers  when  necessary  to 
express  the  denominator,  and  place  the  point  at  the  left. 
There  must  be  as  many  decimal  places  in  the  decimal  as  there 
are  ciphers  in  the  denominator. 

EXAMPLES 
Read  the  following  numbers  : 


1. 

.7 

7. 

.4375 

13. 

.0000054 

19. 

9.999999 

2. 

.07 

8. 

.03125 

14. 

35.18006 

20. 

.10016 

3. 

.007 

9. 

.21875 

15. 

.0005 

21. 

.000155 

4. 

.700 

10. 

.90625 

16. 

100.000104 

22. 

.26 

5. 

.125 

11. 

.203125 

17. 

9.1632002 

23. 

.1 

6. 

.0625 

12. 

.234375! 

18. 

30.3303303 

24. 

.80062 

Express  decimally : 

1.  Four  tenths. 

2.  Three  hundred  twenty-five  thousandths. 

3.  Seventeen  thousand  two  hundred  eleven  hundred-thou- 
sandths. 

4.  Seventeen  hundredths.  6.   Five  hundredths. 

5.  Fifteen  thousandths.  7.    Six  ten-thousandths. 

8.  Eighteen  and  two  hundred  sixteen  hundred-thousandths. 

9.  One  hundred  twelve  hundred-thousandths. 

10.   10  millionths.  11.   824  ten-thousandths. 

12.  Twenty-nine  hundredths. 

13.  324  and  one  hundred  twenty-six  millionths. 

14.  7846  hundred-millionths. 


32          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

1C  563  1  2123         3  2  86  5  4 

16-  -nnnnnnnrj  TO"O>  nnnnr>  TTF>  r^nnnnnr- 

17.  One  and  one  tenth. 

18.  One  and  one  hundred-thousandth. 

19.  One  thousand  four  and  twenty-nine  hundred ths. 

Reduction  of  Decimals 

Ciphers  annexed  to  a  decimal  do  not  change  the  value  .of 
the  decimal;  these  ciphers  are  called  decimal  ciphers.  For 
each  cipher  prefixed  to  a  decimal,  the  value  is  diminished  ten- 
fold. The  denominator  of  a  decimal  —  when  expressed  —  is 
always  1  with  as  many  ciphers  as  there  are  decimal  places  in 
the  decimal. 

To  reduce  a  decimal  to  a  common  fraction. 

Write  the  numerator  of  the  decimal  omitting  the  point  for  the 
numerator  of  the  fraction.  For  the  denominator  write  1  with  as 
many  ciphers  annexed  as  there  are  decimal  places  in  the  decimal. 
Tfien  reduce  to  lowest  terms. 

EXAMPLE.  —  Reduce  .25  and  .125  to  common  fractions. 

1  Write  25  for  the  numerator  and 

0~ 25  2$  1  A                 1  for  the  denominator  with  two  O's, 

~  100  ~~  ^00  ~~  4  "                   which  makes  ^  ;   T^  reduced  to 

4  lowest  terms  is  \. 

1 

H  OK  _  125  _     fflfi  _  1      *  .125  is  reduced  to  a  common  frac- 

=  1000  ~~          )  ~~  8    '  tion  in  the  same  way. 


EXAMPLE.  —  Reduce  .371  to  a  common  fraction. 

37     has  for  its  denominator  1 


=       x-  =       Ans 
100      100       2       ^[00      8    "  This    is    a    complex    fraction 

4  which  reduced  to  lowest  terms 


REVIEW  OF  ARITHMETIC 

EXAMPLES 
Reduce  to  common  fractions  : 


1.  .09375 

6.  2.25 

11.  .16| 

16.  .87J 

2.  .15625 

7.  16.144 

12.  .331 

17.  .66  1 

3.  .015625 

8.  25.0000100 

13.  .061 

18.  .36J 

4.  .609375 

9.  1084.0025 

14.  .140625 

19.  .83^ 

5.  .578125 

10.  .121 

15.  .984375 

20.  .621 

To  reduce  a  common  fraction  to  a  decimal. 

Annex  decimal  ciphers  to  the  numerator  and  divide  by  the  de- 
nominator. Point  off  from  the  right  of  the  quotient  as  many 
places  as  there  are  ciphers  annexed.  If  there  are  not  figures 
enough  in  the  quotient,  prefix  ciphers. 

The  division  will  not  always  be  exact,  i.e.  -f  =  .142f  or  .142+. 

EXAMPLE.  —  Reduce  J  to  a  decimal. 

.75 

4)3.00 
28 

20 
I  =  .75 

EXAMPLES 

Reduce  to  decimals : 

1.    JQ  6.    -I  11.    ¥L  ™>     fi  21.    ^ 

2    irhr          7    ti          12     2To          17-   16i         22-   25.12^ 

3.  ^  8.    If  13.    ^          18.    66|  23.    331 

4.  1  9.    A  14-    12i  19-    if  24-    A 

5.  |  10.    T^          15.    T6T  20.    |  25. 

Addition  of  Decimals 

To  add  decimals,  write  them  so  that  their  decimal  points  are  in 
a  column.  Add  as  in  integers,  and  place  the  point  in  the  sum 
directly  under  the  points  above  it. 


34          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

EXAMPLE.  —  Find  the  sum  of  3,87,2.0983,  5.00831,  .029, 
.831. 

3.87 

2  Q983  Place  these  numbers,  one  under  the  other,  with 

'    ,  decimal  points  in  a  column,  and  add  as  in  addition 

of  integers.     The  sum  of  these  numbers  should 
have  the  decimal  point  in  the  same  column  as  the 
.831  numbers  that  were  added. 

11.83661    Ans. 

EXAMPLES 
Find  the  sum  : 

1.  5.83,  7.016,  15.0081,  and  18.3184. 

2.  12.031,  0.0894,  12.0084,  and  13.984. 

3.  .0765,  .002478,  .004967,  .0007862,  .17896. 

4.  24.36,  1.358,  .004,  and  1632.1. 

5.  .175,  1.75, 17.5,  175.,  1750. 

6.  1.,  .1,  .01,  .001,  100,  10.,  10.1,  100.001. 

7.  Add  5  tenths;  8063  millionths;  25  hundred-thousandths ; 
48  thousandths;    17  millionths;    95  ten-millionths ;   5,  and  5 
hundred-thousandths ;  17  ten-thousandths. 

8.  Add  24f ,  171  .0058,  71,  9Ty 

9.  32.58,  28963.1,  287.531,  76398.9341. 
10.   145.,  14.5, 1.45,  .145,  .0145. 

Subtraction  of  Decimals 

To  subtract  decimals,  write,  the  smaller  number  under  the 
larger  tvith  the  decimal  point  of  the  subtrahend  directly  under  the 
decimal  point  of  the  minuend.  Subtract  as  in  integers,  and  place 
the  point  directly  under  the  points  above. 

EXAMPLE.  —  Subtract  2.17857  from  4.3257. 

Write  the  lesser  number  under  the  greater, 

4.32570  Minuend  with  the  decimal    points  under  each  other. 

2.17857  Subtrahend      Add  a  0  to  the  minuend,  4.3257,  to  give  it  the 
2.14713  Remainder       same,  denominator  as  the  subtrahend.     Then 
subtract  as  in  subtraction  of  integers.     Write 
the  remainder  with  decimal  point  under  the  other  two  points. 


REVIEW  OF  ARITHMETIC  35 

EXAMPLES 

Subtract : 

1.  59.0364-30.8691  =  ?  3.   .0625  -  .03125  =  ? 

2.  48.7209-12.0039  =  ?  4.   .00011  -  .000011  =  ? 

5.  10 -.1  +  . 0001  =  ? 

6.  From  one  thousand  take  five  thousandths. 

7.  Take  17  hundred-thousandths  from  1.2. 

8.  From  17.371  take  14.161. 

9.  Prove  that  1  and  .500  are  equal. 

10.   Find  the  difference  between  y3^4^  and  ^-fl^ff. 

Multiplication  of  Decimals 

To  multiply  decimals  proceed  as  in  integers,  and  give  to  the 
product  as  many  decimal  figures  as  there  are  in  both  multiplier 
and  multiplicand.  When  there  are  not  figures  enough  in  the 
product,  prefix  ciphers. 

EXAMPLE.  —  Find  the  product  of  6.8  and  .63. 

6.8     Multiplicand 

63  Multiplier  6<^  *s  tne  multiplicand  and  .63  the  multiplier. 

~nr\4  Their  product  is  4.284  with  three  decimal  figures, 

the  number  of  decimal  figures  in  the  multiplier 

and  multiplicand. 


4.284  Product 

EXAMPLE.  —  Find  the  product  of  .05  and  .3. 

.05     Multiplicand          The  product  of  .05  and  .3  is  .015  with  a  cipher 
.3     Multiplier  prefixed  to  make  the  three  decimal  figures  re- 

.015  Product  quired  in  the  product. 

EXAMPLES 
Find  the  products : 

1.  46.25  x. 125  3.   .015  x. 05 

2.  8.0625  X  .1875  4.   25.863  x  44- 


36          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

5.  11.11x100  8.    .325xl2| 

6.  .5625  x  6.28125  9.   .001542  x  .0052 

7.  .326  x  2.78  10.   1.001  x  1.01 

To  multiply  by  10,  100,  1000,  etc.,  remove  the  point  one  place 
to  the  right  for  each  cipher  in  the  multiplier. 

This  can  be  performed  without  writing  the  multiplier. 
EXAMPLE.— Multiply  1.625  by  100. 

1.625  x  100  =  162.5 

To  multiply  by  200,  remove  the  point  to  the  right  and  multiply 
by  2. 

EXAMPLE.  — Multiply  86.44  by  200. 

86.44. 

2 

17,288 

EXAMPLES 

Find  the  product  of : 

1.  1  thousand  by  one  thousandth. 

2.  1  million  by  one  millionth. 

3.  700  thousands  by  7  hundred-thousandths. 

4.  3.894  x  3000  5.   1.892  x  2000. 

Division  of  Decimals 

To  divide  decimals  proceed  as  in  integers,  and  give  to  the  quo- 
tient as  many  decimal  figures  as  the  number  in  the  dividend  ex- 
ceeds those  in  the  divisor. 

EXAMPLE.  — Divide  12.685  by  .5. 

The  number  of  decimal  figures  in 

Divisor  .5)12.685  Dividend      the  quotient,  12.685,  exceeds  the  num- 
25.37    Quotient        her  of  decimal  figures  in  the  divisor,  .5, 
by  two.     So  there  must  be  two  deci- 
mal figures  in  the  quotient. 


REVIEW  OF  ARITHMETIC 


37 


EXAMPLE.  —  Divide  399.552  by  192. 

When  the  divisor  is  an  integer, 

2.081  Quotient  tjie  point  jn  the  quotient  should  be 
placed  directly  over  the  point  in 
the  dividend,  and  the  division  per- 
formed as  in  integers.  This  may 
be  proved  by  multiplying  divisor 


Divisor  192)399.552  Dividend 
384 


1555 
1536 


192 
192 


by  quotient,  which  would  give  the 
dividend. 


Divisor  1.25.)28.78.884  Dividend 
250 


EXAMPLE.  —  Divide  28.78884  by  1.25. 

When    the    divisor  contains 

23.031+  Quotient  decimal  figures,  move  the  point 
in  both  divisor  and  dividend  as 
many  places  to  the  right  as 
there  are  decimal  places  in  the 
divisor,  which  is  equivalent  to 
multiplying  both  divisor  and 
dividend  by  the  same  number 
and  does  not  change  the  quo- 
tient. Then  place  the  point  in 
the  quotient  as  if  the  divisor 
were  an  integer.  In  this  ex- 
ample, the  multiplier  of  both 


378 
375 


388 
375 

134 

125 

9  Remainder 


dividend  and  divisor  is  100. 


EXAMPLES 

Find  the  quotients : 

1.  .0625  —  .125  5.  1000  -  .001 

2.  315.432  -  .132  6.  2.496 -.136 

3.  .75 -.0125  7.  28000-16.8 

4.  125-^121 


8.  1.225-4.9 

9.  3.1416-27 
10.   8.33-5 


To  divide  by  10,  100,  1000,  etc.,  remove  the  point  one  place  to 
the  left  for  each  cipher  in  the  divisor. 

To  divide  by  200,  remove  the  point  two  places  to  the  left,  and 
divide  by  2. 


38          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

EXAMPLES 

Find  the  quotients : 

1.  38.64  —  10  6.  865.45-=-  5000 

2.  398.42-1000  7.  38.28-400 

3.  1684.32-1000  8.  2.5-500 

4.  1.155-100  9.  .5-10 

5.  386.54-2000  10.  .001-1000 

REVIEW  EXAMPLES 

1.  Add  28.03,  .1674,  .08309,  7.00091,  .1895. 

2.  Subtract  1.00894  from  13.0194. 

3.  Multiply  83.74  x  3.1416. 

4.  Divide  3.1416  by  8.5. 

5.  Perform  the  following  calculations  :  .7854  x  35  x  7.5. 

6.  Perform  the  following  calculations  : 

65.3  x  3.1416  x  .7854 
600  x  3.5  x  8.3 

7.  Change  the  following  fractions  to  decimals  : 

00   2V    (&)  A,    00   eV  ,    W  yiu>    00  TV,    (/)  A,    (?)  A- 

8.  Change  the  following  decimals  to  common  fractions  : 

(a)  .331     (6)  .25,    (c)  .125,    (d)  .375,    (e)  .437J,    (/)  .875. 

Parts  of  100  or  1000 

1.  What  part  of  100  is  12£  ?  25  ?  33|  ? 

2.  What  part  of  1000  is  125?  250?  333|? 

3.  How  much  is  i  of  100?     Of  1000? 

4.  How  much  is  l  of  100  ?     Of  1000  ? 

5.  What  is  J  of  100  ?     Of  1000? 

EXAMPLE.  —  How  much  is  25  times  24  ? 

100  times  24  =  2400. 
25  times  24  =  1  as  much  as  100  times  24  =  600.    Ans. 


REVIEW  OF  ARITHMETIC  39 

Short  Method  of  Multiplication 

To  multiply  by 

25,  multiply  by  100  and  divide  by  4  ; 
331,  multiply  by  100  and  divide  by  3 ; 
16},  multiply  by  100  and  divide  by  6 ; 
121,  multiply  by  100  and  divide  by  8 ; 
9,  multiply  by  10  and  subtract  the  multiplicand  ; 
11,  if  more  than  two  figures,  multiply  by  10  and  add  the 

multiplicand  to  the  product ; 

11,    if  two  figures,  place  the  figure  that  is  their  sum  between 
them. 

63  x  11  =  693  74  x  11  =  814 

Note  that  when  the  sum  of  the  two  figures  exceeds  nine,  the  one  in  the 
tens  place  is  carried  to  the  figure  at  the  left. 

EXAMPLES 
Multiply  by  the  short  process  : 

1.  81  by  11  =  ?  10.  68  by  16f  =  ? 

2.  75  by  331  =  ?  11.  112  by  11  =  ? 

3.  128  by  12J  =  ?  12.  37  by  11  =  ? 

4.  87  by  11  =  ?  13.  4183  by  11  =  ? 

5.  19  by  9  =  ?  14.  364  by  33i  =  ? 

6.  846  by  11  =  ?  15.  8712  by  121  =  ? 

7.  88  by  11  =  ?  16.  984  by  16}  =  ? 

8.  19  by  11  =  ?  17.  36  by  25  =  ? 

9.  846  by  16}  =  ?  18.  30  by  3331  =  ? 

Aliquot  Parts  of  $1.00 

The  aliquot  parts  of  a  number  are  the  numbers  that  are 
exactly  contained  in  it.  The  aliquot  parts  of  100  are  5,  20, 
121,  16},  331,  etc. 

The  monetary  unit  of  the  United  States  is  the  dollar,  con- 
taining one  hundred  cents,  which  are  written  decimally. 


40          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

6  J  cents  =  $  -^  25    cents  ==  $  1  =  quarter  dollar 

81  cents  =  $  T^  33 J  cents  =  $  1 

12|  cents  =  $  -J-  50    cents  =  $  1  =  half  dollar 
16 J  cents  =  $  1 

10  mills     =  1  cent,  ct.    =  $  .01  or  $  0.01 
5  cents     =  1  "  nickel  "  =  $  .05 
10  cents     =  1  dime,    d.  =  $  .10 
10  dimes    =  1  dollar,  $  =  $  1.00 
10  dollars  =  1  eagle,  E.   =  $  10.00 

EXAMPLE. — What  will  69  pairs  of  stockings  cost  at  16  J 
cents  a  pair  ? 

69  pairs  will  cost  69  x  16f  cts.,  or  69  x  $  \  =  -\9-  =  $  llf  =  $  11.50. 

EXAMPLE.  —  At  25^  a  peck,  how  many  pecks  of  potatoes 
can  be  bought  for  $  8.00  ? 
8-5-^  =  8x^  =  32  pecks.     Ans. 

Review  of  Decimals 

1.  For  work  on  a  job  one  woman  receives  $  13.75,  a  second 
woman  $  12.45,  a  third  woman  $  14.21,  and  a  fourth  woman 
$  21.85.     What  is  the  total  amount  paid  for  the  work  ? 

2.  A  pipe  has  an  inside  diameter  of  3.067  inches  and  an 
outside  diameter  of  3.428  inches.     What  is  the  thickness  of 
the  metal  of  the  pipe  ? 

3.  At  4|  cts.  a  pound,  what  will  be  the  cost  of  108  boxes  of 
salt  each  weighing  29  Ib.  ? 

4.  A   dressmaker   receives    $  121.50   for   doing   a  piece  of 
work.     She  gives  $  12.25  to  one  of  her  helpers  and   $  10.50 
to  another.     She  also  pays  $  75.75  for  material.     How  much 
does  she  make  on  the  job  ? 

5.  An  automobile  runs  at  the  rate  of  91  miles  an  hour. 
How  long  will  it  take  it  to  go  from  Lowell  to  Boston,  a  dis- 
tance of  26.51  miles  ? 


REVIEW  OF  ARITHMETIC  41 

6.  A  man  uses  a  gallon  of  gasoline  in  traveling  16  miles. 
If  a  gallon  costs  23  cents,  what  is  the  cost  of  fuel  per  mile  ? 

7.  Which  is  cheaper,  and  how  much,  to  have  a  13J  cents 
an  hour  woman  take  13^  hours  on  a  piece  of  work,  or  hire  a 
17|  cents  an  hour  woman  who  can  do  it  in  9^  hours  ? 

8.  On  Monday  1725.25  Ib.  of  coal  are  used,  on   Tuesday 
2134.43  Ib.,  on  Wednesday  1651.21  Ib.,  on  Thursday  1821.42 
Ib.,  on  Friday  1958.82  Ib.,  and  on  Saturday  658.32  Ib.     How 
many  pounds  of  coal  are  used  during  the  week  ? 

9.  If,  in  the  example  above,   there  were  10,433.91  Ib.  of 
coal  on  hand  at  the  beginning  of  the  week,  how  much  was  left 
at  the  end  of  the  week  ? 

10.  The  distance  traveled  in  an  automobile  is  measured  by  an 
instrument  called  a  speedometer.    A  man  travels  in  a  week  the 
following  distances:  87.5  mi.,  49.75  mi.,  112.60  mi.,  89.7  mi., 
119.3  mi.,  and  93.75  mi.    What  is  the  total  distance  traveled  ? 

11.  An  English  piece  of  currency  corresponding  to  our  five- 
dollar  bill  is  called  a  pound  sterling  and  is  worth  $4.866|. 
How  much  more  is  a  five-dollar  bill  than  a  pound  ? 

12.  An  alloy  is  made  of  copper  and  zinc.     If  .66  is  copper 
and  .34  is  zinc,  how  many   pounds   of   zinc   and   how   many 
pounds    of   copper   will   there    be   in  a  casting   of  the  alloy 
weighing  98  Ib.  ? 

13.  A  train  leaves  New  York  at  2.10  P.M.  and  arrives  in 
Philadelphia  at  4.15  P.M.     The  distance  is  90  miles.     What  is 
the  average  rate  per  hour  of  the  train  ? 

14.  The  weight  of  a  foot  of  Ty  steel  bar  is  1.08  Ib.     Find 
the  weight  of  a  21-foot  bar. 

15.  A  steam  pump  pumps  3.38  gallons  of   water   to   each 
stroke  and  the  pump  makes  51.1  strokes  per  minute.     How 
many  gallons  of  water  will  it  pump  in  an  hour  ? 

16.  At  121  cents  per  hour,  what  will  be  the  pay  for  23^  days 
if  the  days  are  10  hours  each  ? 


42          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

Compound  Numbers 

A  number  composed  of  different  kinds  of  concrete  units  that 
are  related  is  a  compound  number :  as,  3  bu.  2  pk.  1  qt. 

A  denomination  is  a  name  given  to  a  unit  of  measure  or  of 
weight.  A  number  having  one  or  more  denominations  is  also 
called  a  denominate  number. 

Reduction  is  the  process  of  changing  a  number  from  one 
denomination  to  another  without  changing  its  value. 

Changing  to  a  lower  denomination  is  called  reduction  descend- 
ing :  as,  2  bu.  3  pk.  =  88  qt.  Changing  to  a  higher  denomi- 
nation is  called  reduction  ascending ;  as,  88  qt.  =  2  bu.  3  pk. 

Linear  Measure  is  used  in  measuring  lines  or  distance 

Table 

12  inches  (in.)  =  1  foot,  ft. 

3  feet  =  1  yard,  yd. 

5|  yards,  or  161  feet  =  1  rod,  rd. 
320  rods,  or  5280  feet  =  1  mile,  mi. 
1  mi.  =  320  rd.  =  1760  yd.  =  5280  ft.  =  03,360  in. 

Square  Measure  is  used  in  measuring  surfaces. 

Table 

144  square  inches    =  1  square  foot,  sq.  ft. 

9  square  feet        =  1  square  yard,  sq.  yd. 
30^  square  yards  j  =  l  e  rod         pd 

272£  square  feet     J 
160  square  rods       =  1  acre,  A. 
640  acres  =  1  square  mile,  sq.  mi. 

1  sq.  mi.  =  640  A.  =  102,400  sq.  rd.  =  3,097,600  sq.  yd. 

Cubic  Measure  is  used  in  measuring  volumes  or  solids. 

Table 

1728  cubic  inches  =  1  cubic  foot,  cu.  ft. 

27  cubic  feet  =  1  cubic  yard,  cu.  yd. 

16  cubic  feet  =  1  cord  foot,  cd.  ft. 

8  cord  feet,  or  128  cu.  ft.  =  1  cord,  cd. 
1  cu.  yd.  =  27  cu.  ft.  =  46,656  cu.  in. 


REVIEW  OF  ARITHMETIC  43 

Liquid  Measure  is  used  in  measuring  liquids. 

Table 

4  gills  (gi.)  =  1  pint,  pt. 

2  pints         =  1  quart,  qt. 

4  quarts       =  1  gallon,  gal. 
1  gal.  =  4  qt.  =  8  pt.  =  32  gi. 
A  gallon  contains  231  cubic  inches. 
The  standard  barrel  is  31£  gal.,  and  the  hogshead  63  gal. 

Dry  Measure  is  used  in  measuring  roots,  grain,  vegetables, 
etc. 

Table 

2  pints    =  1  quart,  qt. 
8  quarts  =  1  peck,  pk. 
4  pecks    =  1  bushel,  bu. 
1  bu.  =  4  pk.  =  32  qt.  =  64  pints. 

The   bushel   contains   2150.42  cubic   inches;    1  dry  quart   contains 
67.2  cu.  in.    A  cubic  foot  is  ff  of  a  bushel. 

Avoirdupois  Weight  is  used  in  weighing  all  common  articles  ; 
as,  coal,  groceries,  hay,  etc. 

Table 

16  ounces  (oz.)        =  1  pound,  Ib. 
100  pounds  =  1  hundredweight,  cwt. ; 

or  cental,  ctl. 

20  cwt.,  or  2000  Ib.  =  1  ton,  T. 
1  T.  =  20  cwt.  =  2000  Ib.  =  32,000  oz. 

The  long  ton  of  2240  pounds  is  used  at  the  United  States  Custom 
House  and  in  weighing  coal  at  the  mines. 

Measure  of  Time. 

Table 

60  seconds  (sec.)  =  1  minute,  min. 
60  minutes  =  1  hour,  hr. 

24  hours  =  1  day,  da. 

7  days  =  1  week,  wk. 

365  days  =  1  year,  yr. 

366  days       =  1  leap  year. 
100  years      =  1  century. 


44          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

Counting. 

Table 

12  things  =  1  dozen,  doz. 
12  dozen  =  1  gross,  gr. 
12  gross    =  1  great  gross,  G.  gr. 
Paper  Measure. 

Table 

24  sheets  =  1  quire  2  reams     =  1  bundle 

20  quires  =  1  ream  5  bundles  =  1  bale 

Reduction  Descending 
EXAMPLE.  —  Reduce  17  yd.  2  ft.  9  in.  to  inches. 

1  yd.  =  3  ft. 
17  yd.  =  17  x  3  =  51  ft. 
51  +  2  =  53  ft. 
1  ft.  =  12  in. 

53  ft.  =  53  x  12  =  636  in. 
636  +  9  =  645  in.     Am. 

EXAMPLES 
Reduce  to  lower  denominations : 

1.  46  rd.  4  yd.  2  ft.  to  feet. 

2.  4  A.  15  sq.  rd.  4  sq.  ft.  to  square  inches. 

3.  16  cu.  yd.  25  cu.  ft.  900  cu.  in.  to  cubic  inches. 

4.  15  gal.  3  qt.  1  pt.  to  pints. 

5.  27  da.  18  hr.  49  min.  to  seconds. 

Reduction  Ascending 

EXAMPLE. — Reduce  1306  gills  to  higher  denominations. 

4)1306  gi. Since  in  1  pt.  there  are  4  gi.,  in  1306  gi. 

2)326  pt.  +  2  gi.  there  are  as  many  pints  as  4  gi.  are  contained 

4)163  qt. times  in  1306  gi.,  or  326  pt.  and  2  gi.  remainder. 

40  gal.  +  3  qt.  In  the  same  way  the  quarts  and  gallons  are 

40  gal.  3  qt.  2  gi.  Ans.       found.     So  there  are  in  1306  gi.,  40  gal.  3  qt. 
2gi. 


REVIEW  OF  ARITHMETIC  45 

EXAMPLES 

Reduce  to  higher  denominations  : 

1.  Reduce  225,932  in.  to  miles,  etc. 

2.  Change  1384  dry  pints  to  higher  denominations. 

3.  In  139,843  sq.  in.  how  many  square  miles,  rods,  etc.  ? 

4.  How  many  cords  of  wood  in  3692  cu.  ft.  ? 

5.  How  many  bales  in  24,000  sheets  of  paper  ? 

A  denominate  fraction  is  a  fraction  of  a  unit  of  weight  or 
measure. 

To  reduce  denominate  fractions  to  integers  of  lower  denominations. 

Change  the  fraction  to  the  next  lower  denomination.  Treat 
the  fractional  part  of  the  product  in  the  same  way,  and  so  pro- 
ceed to  the  required  denomination. 

EXAMPLE.  —  Reduce  f  of  a  mile  to  rods,  yards,  feet,  etc. 


f  of  320  rd.  =  -i-6^-0-  rd.  =  228f  rd. 

f  of  V  yd.  =  #  yd.  =  3^  yd. 

\  of  3  ft.  =  Of  ft. 

f  of  12  in.  =  -3/  in.  =  5}  in. 

f  of  a  mile  =  228  rd.  3  yd.  0  ft.  5|  in. 

The  same  process  applies  to  denominate  decimals. 
To  reduce  denominate  decimals  to  denominate  numbers. 
EXAMPLE.  —  Reduce  .87  bu.  to  pecks,  quarts,  etc. 

.87  bu.  .84  qt. 

4  2 

Change  the   decimal    fraction    to 


3.48  pk.  1.68  pt.  the  next  iower  denomination.     Treat 

.48  pk.  the  decimal  part  of  the  product  in  the 

g  same  way,  and  so  proceed  to  the  re- 

o  OA  OJ.  quired  denomination. 

3  pk.  3  qt.  1.68  pt.     Ans. 


46          VOCATIONAL  MATHEMATICS   FOR   GIRLS 

EXAMPLES 

Reduce  to  integers  of  lower  denominations  : 

1.  f  of  an  acre.  3.   ^  of  a  ton. 

2.  .3125  of  a  gallon.  4.    .51625  of  a  mile. 

5.  Change  f  of  a  year  to  months  and  days. 

6.  .2364  of  a  ton. 

7.  What  is  the  value  of  |  of  1^  of  a  mile  ? 

8.  Reduce  -|^  bu.  to  integers  of  lower  denominations. 

9.  .375  of  a  month. 

10.   T9?  acre  are  equal  to  how  many  square  rods,  etc.  ? 

Addition  of  Compound  Numbers 

EXAMPLE.  —  Find  the  sum  of  7  hr.  30  min.  45  sec.,  12  hr. 
25  min.  30  sec.,  20  hr.  15  inin.  33  sec.,  10  hr.  27  mm.  46  sec. 

hr.  min.       sec. 

7  30  45  The  sum  of  the  seconds  =  154  sec.  = 

12  25  30  2  min.  34  sec.     Write  the  34  sec.  under 

20  15  33  the  sec.  column  and  add  the  2  min.  to 

10  27  46  the  min.  column.    Add  the  other  columns 

50  39  34  in  the  same  way. 

50  hr.  39  min.  34  sec.  Ans. 

Subtraction  of  Compound  Numbers 

EXAMPLE.  — From  39  gal.  2  qt.  2  pt.  1  gi.  take  16  gal.  2  qt. 
3  pt.  3  gi. 

.  As  3  gi.  cannot  be  taken  from  1  gi.,  4  gi. 

or  1  pt.  are  borrowed  from  the  pt.  column 

and  added  to  the  1  gi.     Subtract  3  gi.  from 

— —  the  5  gi.  and  the  remainder  is  2  gi.    Continue 

in  the  same  way  until   all   are  subtracted. 
22  gal.  6  qt.  2  gi.  Ans.  22  gal   3  qt  Q  pt  2  gi> 


REVIEW  OF  ARITHMETIC  47 

Multiplication  of  Compound  Numbers 

EXAMPLE.  —  Multiply  4  yd.  2  ft.  8  in.  by  8. 

yd.      ft.     in.  8  times  8  in.  =  64  in.  =  5  ft.  4  in.     Place  the 

428  4  in.  under  the  in.  column,  and  add  the  5  ft.  to 

8_  the  product  of  2  ft.  by  8,  which  equals  21  ft.  =  7  yd. 

39      0      4  Add  7  yd.  to  the  product  of  4  yd.  by  8  =  39  yd. 
39  yd.  4  in.  Ans. 

Division  of  Compound  Numbers 
EXAMPLE.  —  Find  ^  of  42  rd.  4  yd.  2  ft.  8  in. 

rd.      yd.      ft.      in. 

35)42      4      2      8(1  rd. 
35 
7 

6J  -fa  of  42  rd.  =  1  rd. ;   re- 

3£  35)24|(0ft.  mainder,    7    rd.  =  38|   yd.; 

35  12  add  4  yd.  =  42£  yd.     ^  of 

38£  294  42J  yd.  =  1  yd. ;  remainder, 

+  4  +8  7£   yd.,  =  22|    ft.  =  24£   ft. 

35JI2|  yd.  (1  yd.    35)3T)2(8f§  in.  ^  of  24£  ft.  =  0  ft.     24£  ft. 

35_  280  =294  in.  ;  add  8  in.  =302  in. 

~7£  ~22  -s\  of  302  in.  =  8||  in. 

3 

22£  ft.          1  rd.  1  yd.  8f|  in.  Ans. 
12 

Difference  between  Dates 

EXAMPLE. — Find  the  time  from  Jan.  25,  1842,  to  July  4, 
1896. 

1896  74  It  is  customary  to  consider  30  days 

1842  1  25 to  a  month.  July  4,  1896,  is  the  1896th 

54  yr.  6  mo.  9  da.  Ans.  yr.,  7th  mo.,  4th  da.,  and  Jan.  25,  1842, 

is  the  1842d  yr.,   1st.  mo.,  25th  da. 

Subtract,  taking  30  da.  for  a  month. 


48          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

EXAMPLE.  —  What  is  the  exact   number  of  days  between 
Dec.  16,  1895,  and  March  12,  1896  ? 

Dec.   15  Do  not  count  the  first  day  mentioned.    There 

Jan.   31  are  15  days  in  December,  after  the  16th.    Jan- 

Feb.  29  uary  has  31  days,  February  29  (leap  year), 

Mar.  12  and  12  days  in  March  ;  making  87  days. 

87  days.  Ans. 

EXAMPLES 

1.  How  much   time  elapsed  from  the  landing  of  the  Pil- 
grims,  Dec.   11,  1620,  to   the   Declaration  of   Independence, 
July  4,  1776? 

2.  Washington  was  born  Feb.  22,  1732,  and  died  Dec.  14, 
1799.     How  long  did  he  live? 

3.  Mr.  Smith  gave  a  note  dated  Feb.  25,  1896,  and  paid  it 
July  12,  1896.    Find  the  exact  number  of  days  between  its  date 
and  the  time  of  payment. 

4.  A  carpenter  earning  $  2.50  per  day  commenced  Wednes- 
day morning,  April  1, 1896,  and  continued  working  every  week 
day  until  June  6.     How  much  did  he  earn  ? 

5.  Find  the  exact  number  of  days  between  Jan.  10,  1896, 
and  May  5,  1896. 

6.  John  goes  to  bed  at  9.15  P.M.  and  gets  up  at  7.10  A.M. 
How  many  minutes  does  he  spend  in  bed  ? 

To  multiply  or  divide  a  compound  number  by  a  fraction. 

To  multiply  by  a  fraction,  multiply  by  the  numerator,  and 
divide  the  product  by  the  denominator. 

To  divide  by  a  fraction,  multiply  by  the  denominator,  and  divide 
the  product  by  the  numerator. 

When  the  multiplier  or  divisor  is  a  mixed  number,  reduce  to 
an  improper  fraction,  and  proceed  as  above. 


REVIEW   OF  ARITHMETIC  49 

EXAMPLES 

1.  How  much  is  f  of  16  hr.  17  min.  14  sec.  ? 

2.  A  field  contains  10  A.  12  sq.  rd.  of  land,  which  is  f 
of  the  whole  farm.     Find  the  size  of  the  farm. 

3.  If  a  train  runs  60  mi.  35  rd.  16  ft.  in  one  hour,  how  far 
will  it  run  in  12f  hr.  at  the  same  rate  of  speed  ? 

4.  Divide  14  bu.  3  pk.  6  qt.  1  pt.  by  }. 

5.  Divide  5  yr.  1  mo.  1  wk.  1  da.  1  hr.  1  min.  1  sec.  by  3f . 

REVIEW  EXAMPLES 

1.  A  time  card  on  a  piece  of  work  states  that  2  hours  and 
15  minutes  were  spent  on  a  skirt,  1  hour  and  12  minutes  on  a 
waist,  2  hours  and  45  minutes  on  a  petticoat,  and  1  hour  and 
30  minutes  on  a  jacket.     What  was  the  number  of  hours  spent 
on  all  the  work  ? 

2.  How  many  parts  of  a  sewing  machine,  each  weighing  14 
oz.,  can  be  obtained  from  860  Ib.  of  metal  if  nothing  is  allowed 
for  waste  ? 

3.  How  many  feet  long  must  a  dry  goods  store  be  to  hold 
a  counter  8'  6",  a  bench  14'  4",  a  desk  4'  2",  and  a  counter 
7'  5",  placed  side  by  side,  if  3'  3"  are  allowed  between  the 
pieces  of  furniture  and  between  the  walls  and  the  counters  ? 

4.  How  many  gross  in  a  lot  of  968  buttons  ? 

5.  Find  the  sum  of  7  hr.  30  min.  45  sec.,  12  hr.  25  min. 
30  sec.,  20  hr.  15  min.  33  sec.,  10  hr.  27  min.  46  sec. 

6.  If  a  train  is  run  for  8  hr.  at  the  average  rate   of  50 
mi.  30  rd.  10  ft.  per  hour,  how  great  is  the  distance  covered  ? 

7.  A  telephone  pole  is  31  ft.  long.     If  4  ft.  7  in.  are  under 
ground,  how  high  (in  inches)  is  the  top  of  the  pole  above  the 
street  ? 

8.  If  100  bars  of  iron,  each  2f  long,  weigh  70  Ib.,  what  is 
the  total  weight  of  2300  bars  ? 


50          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

9.    If  a  cubic  foot   of   water   weighs   62^  lb.,  how  many 
ounces  does  it  weigh  ? 

10.  A  farmer's  wife  made  9  pounds  7  ounces  of  butter  and 
sold  it  at  41  cents  a  pound.     How  much  did  she  receive  ? 

11.  A  peck  is  what  part  of  a  bushel  ? 

12.  A  quart  is  what  part  of  a  bushel  ?  of  a  peck  ? 

13.  I  have  84  lb.  14  oz.  of  salt  which  I  wish  to  put  into 
packages   of  2   lb.   6   oz.   each.      How   many   packages   will 
there  be  ? 

14.  If  one  bottle  holds  1  pt.  3  gi.,  how  many  dozen  bottles 
will  be  required  to  hold  65  gal.  2  qt.  1  pt.  ? 

15.  How  many  pieces  51"  long  can  be  cut  from  a  rod  16'  8" 
long,  if  5"  are  allowed  for  waste  ? 

16.  What  is  the  entire  length  of  a  .railway  consisting  of  five 
different  lines  measuring  respectively  160  mi.  185  rd.  2  yd., 
97  mi.  63  rd.  4  yd.,  126  mi.  272  rd.  3  yd.,  67  mi.  199  rd.  5  yd., 
and  48  ini.  266  rd.  5  yd.  ? 

Percentage 

Percentage  is  a  process  of  solving  questions  of  relation  by 
means  of  hundredths  or  per  cent  (%). 

Every  question  in  percentage  involves  three  elements :  the 
rate  per  cent,  the  base,  and  the  percentage. 

The  rate  per  cent  is  the  number  of  hundredths  taken. 

The  base  is  the  number  of  which  the  hundredths  are  taken. 

The  percentage  is  the  result  obtained  by  taking  a  certain  per 
cent  of  a  number. 

Since  the  percentage  is  the  result  obtained  by  taking  a  cer- 
tain per  cent  of  a  number,  it  follows  that  the  percentage  is  the 
product  of  the  base  and  the  rate.  The  rate  and  base  are  always 
factors,  the  percentage  is  the  product. 

EXAMPLE.  —  How  much  is  8  %  of  $  200  ? 

8  %  of  $200  =  200  x  .08  =  $  16.  (1) 


REVIEW  OF  ARITHMETIC  51 

In  (1)  we  have  the  three  elements:  8%  is  the  rate,  $200  is  the  base, 
and  $  16  is  the  percentage. 

Since  $  200  x  .08  =  $  16,  the  percentage  ; 

$  16  -=-  .08  =  $  200,  the  base  ; 
and  $  16  -^  $  200  =  .08,  the  rate. 

If  any  two  of  these  elements  are  given,  the  other  may  be 

found  : 

Base  x  Rate  =  Percentage 

Percentage  -5-  Rate  =  Base 
Percentage  -5-  Base  =  Rate 

Per  cent  is  commonly  used  in  the  decimal  form,  but  many 
operations  may  be  much  shortened  by  using  the  common  frac- 
tion form. 

1  %  =    .01  =  T^  i  %  =  .001  or  .005 

10%=    .10  =  A  33|%=.33i  =  | 

100  %  =  LOO  =  1  81  %  =  -081  =  .0825 
121  %  =  .12J  or  .125  =  1  1  %  =  .00  J-  =  .00125 

There  are  certain  per  cents  that  are  used  so  frequently  that 
we  should  memorize  their  equivalent  fractions. 


10= 


20%=  I 
25%  =} 


37*%=  I 

40%  =| 
50%  =  J 
60%=  f 

75  %  =  } 
80%=* 

s4%=I 

EXAMPLES 

1.  Find  75  %  of  $  368. 

2.  Find  15  %  of  $  412. 

3.  840  is  331  %  of  what  number  ? 

4.  615  is  15  %  of  what  number  ? 

5.  What  per  cent  of  12  is  8  ? 


52          VOCATIONAL  MATHEMATICS  FOR  GIRLS 

6.  What  per  cent  of  a  foot  is  8  inches  ?  11  inches  ?  4  inches  ? 

7.  A  technical  high  school  contains  896  pupils  ;  476  of  the 
pupils  are  girls.     What  per  cent  of  the  school  is  girls  ? 

8.  Out   of  a  gross   of  bottles  of  mucilage  9  were  broken. 
What  was  the  per  cent  broken  ? 

Trade  Discount 

Merchants  and  jobbers  have  a  price  list.  From  this  list 
they  give  special  discounts  according  to  the  credit  of  the  cus- 
tomer and  the  amount  of  supplies  purchased,  etc.  If  they 
give  more  than  one  discount,  it  is  understood  that  the  first 
means  the  discount  from  the  list  price,  while  the  second  denotes 
the  discount  from  the  remainder. 

EXAMPLES 

1.  What  is  the  price  of  200  spools  of  cotton  at  $  36.68  per 
M.  at  40  %  off  ? 

2.  Supplies  from  a  dry  goods  store  amounted  to  $  58.75.     If 
121  %  Were  allowed  for  discount,  what  was  the  amount  paid  ? 

3.  A  dealer  received   a  bill  amounting  to  $  212.75.      Suc- 
cessive   discounts    of    15%,   10%,   and    5%    were    allowed. 
What  was  the  amount  to  be  paid  ? 

4.  2  %  is  usually  discounted  on  bills  paid  within  30  days. 
If  the  following  are  to  be  paid  within  30  days,  what  will  be 
the  amounts  due  ? 

a.  $     30.19  c.    $399.16  e.    $1369.99 

b.  2816.49  d.      489.01  /.         918.69 

5.  Millinery  supplies  amounted  to  $  127.79  with  a  discount 
of  40  %  and  15  %.     What  was  the  net  price  ? 

6.  What  single  discount  is  equivalent  to  a  discount  of  45  % 
and  10  %  ? 

7.  What  single  discount  is  equivalent  to  20  %,  and  10  %  ? 


REVIEW   OF  ARITHMETIC  53 

Simple  Interest 

Money  that  is  paid  for  the  use  of  money  is  called  interest. 
The  money  for  the  use  of  which  interest  is  paid  is  called  the 
principal,  and  the  sum  of  the  principal  and  interest  is  called 
the  amount. 

Interest  at  6  %  means  6  %  of  the  principal  for  1  year  ;  12 
months  of  30  days  each  are  usually  regarded  as  a  year  in  com- 
puting interest.  There  are  several  methods  of  computing 
interest. 

EXAMPLE. — What  is  the  interest  on  $  100  for  3  years  at  6  %  ? 

$100 
.06 

$  6.00  interest  for  one  year.  Or,  ^fa  x  ^  x  f  =  $18.     Ans. 

3 


$  18.00  interest  for  3  years.     Ans. 

$  100  +  $  18  =  $  118,  amount. 

Principal  x  Rate  x  Time  =  Interest. 

EXAMPLE.  —  What  is  the  interest  on  $  297.62  for  5  yr.  3  mo. 

at  6  %  ? 

$297.62  3 

.06        nr      0    w  $  297.62  ^  21  _  $  18750.06  _  ^  09  7* 

yjL »    TTT^  *  ~~     ~+ *  ~V  —   ^7 —  '1?  vo> '  o> 


$17.8572  100  1  £  200 

5j  2 

4.4643 
89.2860  NOTE.  —Final  results  should  not  include 


$93.7503    $93.75.    Ans.        mills.     Mills  are  disregarded  if  less  than  5, 
and  called  another  cent  if  5  or  more. 

EXAMPLES 

1.  What  is  the  interest  on  $  586.24  for  3  months  at  6  %  ? 

2.  What  is  the  interest  on  $  816.01  for  9  months  at  5  %  ? 

3.  What  is  the  interest  011  $  314.72  for  1  year  at  4  %  ? 

4.  What  is  the  interest  on  $  876.79  for  2  yr.  3  mo.  at  4£  %  ? 

5.  What  is  the  interest  on  $  2119.70  for  6  yr.  -2  mo.  13  da. 
at  51  %  ? 


54         VOCATIONAL  MATHEMATICS  FOR   GIRLS 

The  Six  Per  Cent  Method 

By  the  6  %  method  it  is  convenient  to  find  first  the  interest 
of  $  1,  then  multiply  it  by  the  principal. 

EXAMPLE,  —r  What  is  the  interest  on  $  50.24  at  6  %  for  2  yr. 
8  mo.  18  da.  ? 

Interest  on  $  1  for  2  yr.  =2  x  $  .06  =  $ .  12 
Interest  on  $  1  for  8  mo.  =  8  x  $  .OOJ  =  .04 
Interest  on  $  1  for  18  da.  =  18  x  $  .000*  -  .003 
Interest  on  $  1  for  2  yr.  8  mo.  18  da.  $  .163 
Interest  on  $  50.24  is  50.24  times  $  .163  =  $  8.19.  Ans. 

Second  Method.  —  Interest  on  any  sum  for  60  days  at  6  %  is 
•j-J-g-  of  that  sum  and  may  be  expressed  by  moving  the  decimal  point 
two  places  to  the  left.  The  interest  for  6  days  may  be  expressed 
by  moving  the  decimal  three  places  to  the  left. 

EXAMPLE.  —  What  is  the  interest  on  $  394.50  for  96  days  at 
6%? 

$3.9450,  interest  on  $394.50  for  60  days  at  6  %. 
1.9725,  interest  on  $394.50  for  30  days  at  6  °Jo. 
.3945,  interest  on  $  394.50  for  6  days  at  6  °Jo. 
$6.3120,  interest  on  $394.50  for  96  days  at  6  %.     Ans.     $  6.31. 

EXAMPLE.  — What  is  the  interest  on  $  529.70  for  78  days  at 
8%? 

$5.297,  interest  on  $529.70  for  60  days  at  6  %. 

1.589,  interest  on  $  529.70  for  18  days  (6  days  x  3) . 
$6.886,  interest  on  $  529.70  for  78  days  at  6  %. 
8  %  =6  %  +£  of  6%. 
$6.886 +  $2.295  =  $9.181.     Ans.  $9.18. 

EXAMPLES 

Find  the  interest  and  amount  of  the  following : 

1.  $  2350  for  1  yr.  3  mo.  6  da.  at  6  %. 

2.  $  125.75  for  2  yr.  5  mo.  17  da.  at  7  %. 

3.  $  950.63  for  3  yr.  7  mo.  21  da.  at  5  %. 

4.  $  625.57  for  2  yr.  8  mo.  28  da.  at  8  %. 


REVIEW  OF  ARITHMETIC  55 

Exact  Interest 

When  the  time  includes  days,  interest  computed  by  the  6% 
method  is  not  strictly  exact,  by  reason  of  using  only  30  days 
for  a  month,  which  makes  the  year  only  360  days.  The  day  is 
therefore  reckoned  as  -^  of  a  year,  whereas  it  is  -^  of  a  year. 

To  compute  exact  interest,  find  the  exact  time  in  days,  and  con- 
sider 1  day's  interest  as  ^-^  of  1  year's  interest. 

EXAMPLE.  —  Find  the  exact  interest  of  $  358  for  74  days  at 

7%. 

$358  x  .07  =  $25.06,  1  year's  interest. 
74  days'  interest  is  -/^  of  1  year's  interest. 
^  of  $  25.06  =  $  5.08.    Ans. 
Qr   $358      _7_      J74  _  , 
1     X100      365~ 

EXAMPLES 

Find  the  exact  interest  of : 

1.  $324  for  15  da.  at  5  %. 

2.  $253  for  98  da.  at  4%. 

3.  $624  for  117  da.  at  7  %. 

4.  $  620  from  Aug.  15  to  Nov.  12  at  6  %. 

5.  $  153.26  for  256  da.  at  5|  %  • 

6.  $  540.25  from  June  12  to  Sept.  14  at  8  %. 

Rules  for  Computing  Interest 

The  following  will  be  found  to  be  excellent  rules  for  finding  the  inter- 
est on  any  principal  for  any  number  of  days. 

Divide  the  principal  by  100  and  proceed  as  follows: 

2  %  — Multiply  by  number  of  days  to  run,  and  divide  by  180. 
21  %  —  Multiply  by  number  of  days,  and  divide  by  144. 

3  %  —  Multiply  by  number  of  days,  and  divide  by  120. 

3*  °l°  —  Multiply  by  number  of  days,  and  divide  by  102.86. 


56 


VOCATIONAL  MATHEMATICS   FOR   GIRLS 


4  %  —  Multiply  by  number  of  days,  and  divide  by  90. 

5  %  —  Multiply  by  number  of  days,  and  divide  by  72. 

6  %  —  Multiply  by  number  of  days,  and  divide  by  60. 

7  %  —  Multiply  by  number  of  days,  and  divide  by  51.43. 

8  %  — Multiply  by  number  of  days,  and  divide  by  45. 

Savings  Bank  Compound  Interest  Table 

Showing  the  amount  of  §  1,  from  1  year  to  15  years,  with  compound 
interest  added  semiannually,  at  different  rates. 


PER  CENT 

3 

4 

5 

6 

7 

8 

9 

iyear 

1  01 

102 

102 

1  03 

03 

1  04 

104 

1    year 

1  03 

104 

1  05 

1  06 

07 

1  08 

109 

1^  years 

104 

1  06 

107 

109 

10 

112 

1  14 

2    years 

106 

108 

1  10 

1  12 

14 

116 

1  19 

2|  years 

1  07 

1  10 

1  13 

1  15 

18 

1  21 

1  24 

3    years 

1  09 

1  12 

1  15 

1  19 

22 

1  26 

130 

3|  years 

1  10 

1  14 

1  18 

1  22 

27 

1  31 

136 

4    years 

1  12 

1  17 

1  21 

1  26 

131 

1  36 

1  42 

4^  years 

1  14 

1  19 

124 

1  30 

1  36 

1  42 

1  48 

5    years 

1  16 

1  21 

128 

1  34 

41 

148 

1  55 

5J  years 

1  17 

1  24 

131 

138 

45 

153 

1  62 

6    years 

1  19 

1  26 

1  34 

142 

51 

1  60 

169 

Q\  years 

1  21 

1  29 

1  37 

146 

56 

1  66 

1  77 

7    years 

123 

1  31 

1  41 

1  51 

61 

1  73 

185 

7|  years 

1  24 

1  34 

144 

1  55 

67 

1  80 

1  93 

8    years 

1  26 

1  37 

148 

1  60 

73 

1  87 

202 

8|  years 

128 

139 

1  52 

1  65 

79 

1  94 

2  11 

9    years 

1  30 

142 

1  55 

170 

85 

202 

220 

9|  years 

132 

1  45 

1  59 

175 

92 

2  10 

230 

10    years 

1  34 

1  48 

163 

1  80 

98 

2  19 

241 

11    years 

1  38 

1  54 

1  72 

1  91 

2  13 

236 

263 

12    years 

1  42 

1  60 

1  80 

203 

228 

256 

287 

13    years 

1  47 

167 

190 

2  15 

2  44 

277 

314 

14    years 

1  51 

1  73 

199 

228 

2  62 

299 

342 

15    years 

1  56 

1  80 

209 

242 

280 

324 

374 

REVIEW  OF  ARITHMETIC  57 

EXAMPLES 

Solve  the  following  problems  by  using  the  tables  on  page  56  : 

1.  What  is   the  compound  interest  of   $1   at  the  end  of 
81  years  at  6  %  ? 

2.  What  is  the  compound  interest  of  $  1  at  the  end  of  11 
years  at  6  °/0  ? 

3.  How  long  will  it  take   $  400  to  double  itself  at  5  % , 
compound  interest? 

4.  How  long  will  it  take  $  580  to  double  itself  at  5£  % , 
compound  interest  ? 

5.  How  long  will   it  take   $615  to  double  itself  at  8  %, 
simple  interest? 

6.  How  long  will  it  take   $784  to  double  itself   at  7%, 
simple  interest  ? 

7.  Find  the  interest  of  $  684  for  94  days  at  3  %. 

8.  Find  the  interest  of  $  1217  for  37  days  at  4  %. 

9.  Find  the  interest  of  $681.14  for  74  days  at  4|-  %. 

10.  Find  the  interest  of  $414.50  for  65  days  at  5  %. 

11.  Find  the  interest  of  $384.79  for  115  days  at  6  %. 

Ratio  and  Proportion 

Ratio  is  the  relation  between  two  numbers.  It  is  found 
by  dividing  one  by  the  other.  The  ratio  of  4  to  8  is  4  ^-  8  =  i. 

The  terms  of  the  ratio  are  the  two  numbers  compared.  The 
first  term  of  a  ratio  is  the  antecedent,  and  the  second  the  con- 
sequent. The  sign  of  the  ratio  is  (:).  (It  is  the  division  sign 
with  the  line  omitted.)  Ratio  may  also  be  expressed  fraction- 
ally, as  i£  or  16  :  4 ;  or  T3T  or  3  : 17. 

A  ratio  formed  by  dividing  the  consequent  by  the  antece- 
dent is  an  inverse  ratio :  12 :  6  is  the  inverse  ratio  of  6  : 12. 

The  two  terms  of  the  ratio  taken  together  form  a  couplet. 


58          VOCATIONAL  MATHEMATICS   FOR   GIRLS 

Two  or  more  couplets  taken  together  form  a  compound  ratio. 

Thus,  2:5         6:11 

A  compound  ratio  may  be  changed  to  a  simple  ratio  by 
taking  the  product  of  the  antecedents  for  a  new  antecedent, 
and  the  product  of  the  consequents  for  a  new  consequent  ;  as, 
6x2:11x5,  or  12:55. 

Antecedent  -+-  Consequent  =  Eatio 

Antecedent  -+-  Ratio  =  Consequent 
Ratio  x  Consequent  =  Antecedent 

To  multiply  or  divide  both  terms  of  a  ratio  by  the  same 
number  does  not  change  the  ratio. 

Thus  12  :  6  =  2 

3x12:3x6  =  2 


EXAMPLES 

Find  the  ratio  of 

1.  20  :  300  Fractions  with  a  common  de- 

2.  3  bu.  :  3  pk.  nominator  have  the  same 
3    21-16  ratio  as  their  numerators. 

«•    12:i  »•    A:*f  «:*»**'** 

5-    i'*  &    f:|,f:|,|:| 

6.    16:  (?)=!• 

Proportion 

An  equality  of  ratios  is  a  proportion. 

A  proportion  is  usually  expressed  thus  :  4  :  2  :  :  12  :  6,  and  is 
read  4  is  to  2  as  12  is  to  6. 

A  proportion  has  four  terms,  of  which  the  first  and  third  are 
antecedents  and  the  second  and  fourth  are  consequents.  The 
first  and  fourth  terms  are  called  extremes,  and  the  second  and 
third  terms  are  called  means. 

The  product  of  the  extremes  equals  the  product  of  the 
means. 


REVIEW  OF  ARITHMETIC  59 

To  find  an  extreme,  divide  the  product  of  the  means  by  the  given 
extreme. 

To  find  a  mean,  divide  the  product  of  the  extremes  by  the  given 
mean. 

EXAMPLES 

Supply  the  missing  term  : 

1.  1 :  836  : :  25  :  (  )  4.    10  yd.  :  50  yd.  :  :  $  20  :  ($   ) 

2.  6:24::(  )  :  40  5.    $f  :$3f  ::(  ):5 

3.  (  )  :  15  :  :  60 :  6 

Simple  Proportion 

An  equality  of  two  simple  ratios  is  a  simple  proportion. 
EXAMPLE.  —  If  12  bushels  of  charcoal  cost  $  4,  what  will  60 
bushels  cost  ? 

There  is  the  same  relation  between  the  cost 
of  12  bu.  and  the  cost  of  60  bu.  as  there  is  be- 
tween  the  12  bu.  and  the  60  bu.  $4  is  the 
third  term.  The  answer  is  the  fourth  term. 
It  must  form  a  ratio  of  12  and  60  that  shall  equal  the  ratio  of  $  4  to  the 
answer.  Since  the  third  term  is  less  than  the  required  answer,  the  first 
must  be  less  than  the  second,  and  12  :  60  is  the  first  ratio.  The  product 
of  the  means  divided  by  the  given  extreme  gives  the  other  extreme,  or  $  20. 

EXAMPLES 

Solve  by  proportion : 

1.  If  150  yd.  of  edging  cost  $  6,  how  much  will  1200  yd.  cost  ? 

2.  If  250  pounds  of  lead  pipe  cost  $  15,  how  much  will  1200 
pounds  cost  ? 

3.  If  5  men  can  dig  a  ditch  in  3  days,  how  long  will  it  take 
2  men? 

4.  If  4  men  can  shingle  a  shed  in  2  days,  how  long  will  it 
take  3  men  ? 

5.  The  ratio  of  Simon's  pay  to  Matthew's  is  -f.      Simon 
earns  $  18  per  week.     What  does  Matthew  earn  ? 


60          VOCATIONAL  MATHEMATICS  FOR  GIRLS 

6.  What  will  11 1  yards  of  cambric  cost  if  50  yards  cost 
$6.75? 

7.  If  it  takes  7-J-  yards  of  cloth,  1  yard  wide,  to  make  a 
suit,  how  many  yards  of  cloth,  44  inches  wide,  will  it  take  to 
make  the  same  suit  ? 

8.  If  21  yards  of  silk  cost  $  52.50,  what  will  35  yards  cost  ? 

9.  A  farm  valued  at  $5700  is  taxed  for  $38.19.     What 
should  be  the  tax  on  property  valued  at  $  28,500  ? 

10.  If  there  are  7680  minims  in  a  pint  of  water,  how  many 
pints  are  there  in  16,843  minims  ? 

11.  There  are  approximately  15  grains    in  a  gram.     How 
many  grams  in  641  grains  ? 

12.  In  a    velocity   diagram  a  line  '3J   in.  long   represents 
45  ft.     What  would  be  the  length  of  a  line  representing  30  ft. 

velocity  ? 

13.  When  a  post  11.5  ft.  high  casts  a  shadow  on  level  ground 
20.6  ft.  long,  a  telephone  pole  nearby  casts  a  shadow  59.2  ft. 
long.     How  high  is  the  pole  ? 

14.  If  10  grams  of  silver  nitrate  dissolved  in  100  cubic  cen- 
timeters of  water  will  form  a  10  %  solution,  how  much  silver 
nitrate  should  be  used  in  1560  cubic  centimeters  of  water  ? 

15.  A  ditch  is  dug  in  14  days  of  8  hours  each.     How  many 
days  of  10  hours  each  would  it  have  taken  ? 

16.  If  in  a  drawing  a  tree  38  ft.  high  is  represented  by  1^", 
what  on  the  same  scale  will  represent  the  height  of  a  house 
47ft.  high? 

17.  What  will  be  the  cost  of  21  motors  if  15  motors  cost 

$887? 

18.  If  goods  are  bought  at  a  discount  of  25  %  and  are  sold 
at  the  list  price,  what  per  cent  is  gained  ?     (Assume  $  1  as 
the  list  price.) 


REVIEW   OF  ARITHMETIC  61 

18.  If  a  sewing  machine  sews  26  inches  per  minute  on  heavy 
goods,  how  many  yards  will  it  sew  in  an  hour  ? 

19.  If  a  girl  spends  28  cents  a  week  for  confectionery,  how 
much  does  she  spend  for  it  in  three  months  ? 

20.  If  a  pole  8  ft.  high  casts  a  shadow  4J  ft.  long,  how  high 
is  a  tree  which  casts  a  shadow  48  ft.  long  ? 

Involution 

The  product  of  equal  factors  is  a  power. 

The  process  of  finding  powers  is  involution. 

The  product  of  two  equal  factors  is  the  second  power,  or 
square,  of  the  equal  factor. 

The  product  of  three  equal  factors  is  the  third  power,  or  cube, 
of  the  factor. 

42  =  4  x  4  is  4  to  the  second  power,  or  the  square  of  4. 

23  =  2  x  2  x  2  is  2  to  the  third  power,  or  the  cube  of  2. 

34  =3x3x3x3  is  3  to  the  fourth  power,  or  the  fourth  power  of  4. 

EXAMPLES 

Find  the  powers : 

1.  53  3.   I4  5.   (2i)2  7.   93 

2.  1.1s  4.   252  6.   24  8.    .152 

Evolution 

One  of  the  equal  factors  of  a  power  is  a  root. 

One  of  two  equal  factors  of  a  number  is  the  square  root. 

One  of  three  equal  factors  of  a  number  is  the  cube  root  of  it. 

The  square  root  of  16  =  4.     The  cube  root  of  27  =  3. 

The  radical  sign  (^/)  placed  before  a  number  indicates  that 
its  root  is  to  be  found.  The  radical  sign  alone  before  a  number 
indicates  the  square  root. 

Thus,  \/9  =  3  is  read,  the  square  root  of  9  =  3. 


62          VOCATIONAL  MATHEMATICS  FOR  GIRLS 

A  small  figure  placed  in  the  opening  of  the  radical  sign  is 
called  the  index  of  the  root,  and  shows  what  root  is  to  be 
taken. 

Thus,  \/8  =  2  is  read,  the  cube  root  of  8  is  2. 

Square  Root 

The  square  of  a  number  composed  of  tens  and  units  is  equal 
to  the  square  of  the  tens,  plus  twice  the  product  of  the  tens  by 
the  units,  plus  the  square  of  the  units. 

tens'2  +  2  x  tens  X  units  +  units2 

EXAMPLE.  —  What  is  the  square  root  of  1225? 

12'25(30  +  5  =  35  Separating 

Tens2,  302  =       900  into  periods  of 

2xtens  =  2x3Q  =  60[~325  two     figures 

2  x  tens  +  units  =  2  x  30  +  5  =  65 1 325  each  ,     by     a 

checkmark  ('), 

beginning  at  units,  we  have  12'25.     Since  there  are  two  periods  in  the 
power,  there  must  be  two  figures  in  the  root,  tens  and  units. 

The  greatest  square  of  even  tens  contained  in  1225  is  900,  and  its 
square  root  is  30  (3  tens).  Subtracting  the  square  of  the  tens,  900,  the 
remainder  consists  of  2  x  (tens  x  units)  +  units. 

325,  therefore,  is  composed  of  two  factors,  units  being  one  of  them, 
and  2  x  tens  —  units  being  the  other.  But  the  greater  part  of  this  factor 
is  2  x  tens  (2  x  30  =  60).  By  trial  we  divide  325  by  60  to  find  the  other 
factor  (units),  which  is  5,  if  correct.  Completing  the  factor,  we  have 
2  x  tens  +  units  =  65,  which,  multiplied  by  the  other  factor,  5,  gives  325. 
Therefore  the  square  root  is  30  +  5  =  35. 

The  area  of  every  square  surface  is  the  product  of  two  equal 
factors,  length,  and  width. 

Finding  the  square  root  of  a  number,  therefore,  is  equivalent 
to  finding  the  length  of  one  side  of  a  square  surface,  its  area 
being  given. 

1.  Length  x  Width  =  Area 

2.  Area     -r-  Length  =  Width 

3.  Area    -r-  Width  =  Length 


REVIEW   OF  ARITHMETIC  63 

SHORT  METHOD 

EXAMPLE.  —  Find  the  square  root  of  1306.0996. 

13'06. 09'96  (36. 14  Beginning  at  the  decimal  point,  separate  the 

9  number  into  periods  of  two  figures  each,  point- 


66)  406  ing  whole  numbers  to  the  left  and  decimals  to 

396  the  right.     Find  the  greatest  square  in  the  left- 

721)1009  hand  period,  and  write  its  root  at  the  right. 

721  Subtract  the  square  from  the  left-hand  period, 

7224)28896  and  bring  down  the  next  period  for  a  dividend. 

28896  Divide    the  dividend,    with   its   right-hand 

figure  omitted,  by  twice  the  root  already  found, 

and  annex  the  quotient  to  the  root,  and  to  the  divisor.  Multiply  this 
complete  divisor  by  the  last  root  figure,  and  bring  down  the  next  period 
for  a  dividend,  as  before. 

Proceed  in  this  manner  till  all  the  periods  are  exhausted. 
When  0  occurs  in  the  root,  annex  0  to  the  trial  divisor,  bring  down 
the  next  period,  and  divide  as  before. 

If  there  is  a  remainder  after  all  the  periods  are  exhausted,  annex  deci- 
mal periods. 

If,  after  multiplying  by  any  root  figure,  the  product  is  larger  than  the 
dividend,  the  root  figure  is  too  large  and  must  be  diminished.  Also  the 
last  figure  in  the  complete  divisor  must  be  diminished. 

For  every  decimal  period  in  the  power,  there  must  be  a  decimal  figure 
in  the  root.  If  the  last  decimal  period  does  not  contain  two  figures, 
supply  the  deficiency  by  annexing  a  cipher. 

EXAMPLES 
Find  the  square  root  of : 


1.   8836  5.   \7xn  9.    V3.532-6.28 


2.  370881  6.   72.5  10.    V625  +  1296 

3.  29.0521  7.    .009^  11.   _LX  — 

4.  46656  8.   1684.298431          12. 


13.   What.is  the  length  of  one  side  of  a  square  field  that  has 
an  area  equal  to  a  field  75  rd.  long  and  45  rd.  wide  ? 


CHAPTER   II 
MENSURATION 

The  Circle 

A  circle  is  a  plane  figure  bounded  by  a  curved  line,  called 
the  circumference,  every  point  of  which  is  equidistant  from  the 
center. 

The  diameter  is  a  straight  line  drawn, 
from  one  point  of  the  circumference 
to  another  and  passing  through  the 
center. 

The  ratio  of  the  circumference  to 
the  diameter  of  any  circle  is  always  a 
constant  number,  3.1416+,  approxi- 
mately 3|,  which  is  represented  by 
the  Greek  letter  TT  (pi). 

C  =  Circumference 
D  =  Diameter 


The  radius  is  a  straight  line  drawn  from  the  center  to  the 
circumference. 

Any  portion  of  the  circumference  is  an  arc. 

By  drawing  a  number  of  radii  a  circle  may  be  cut  into  a 
series  of  figures,  each  one  of  which  is  called  a  sector.  The  area 
of  each  sector  is  equal  to  one  half  the  product  of  the  arc  and 
radius.  Therefore  the  area  of  the  circle  is  equal  to  one  half  of 
the  product  of  the  circumference  and  radius. 

1  See  Appendix  for  explanation  and  directions  concerning  the  use  of  formulas. 

64 


MENSURATION  65 


R  X        = 


In  this   formula  A  equals   area,  TT  =  3.1416,  and   R1  =  the 
radius  squared. 

^  =  iz>x|<7 

In  this  formula  D  equals  the  diameter  and  C  the  circum- 
ference, 

A=._V  =  3.1416  g=.7864ly 
4  4 

EXAMPLE.  —  What  is  the  area  of   a  circle  whose  radius  is 
3ft.? 


.  ft 


EXAMPLE.  —  What  is  the  area  of  a  circle  whose  circumfer- 
ence is  10  ft.  ? 


X^X  10  =  -^—  =  7.1  sq.ft. 


2      3.1416      2  3.1416 

Area  of  a  Ring.  —  On  examining  a  flat  iron  ring  it  is  clear  that 

the  area  of  one  side  of  the  ring  may  be  found  by  subtracting 

the  area  of  the  inside  circle  from  the  area  of  the  outside  circle. 

Let  D  =  outside  diameter 

d  =  inside  diameter 

A  =  area  of  outside  circle 

a  =  area  of  inside  circle 

(1)  A 


66 


VOCATIONAL  MATHEMATICS  FOR   GIRLS 


(2) 


(3)    A-a  =        - 

4         4 


Let  B  =  area  of  circular  ring  =  A  —  a 


=  —  -c     =  ^Dz-d    =  .7854    D2  - 


EXAMPLE.  —  If  the  outside  diameter  of  a  flat  ring  is  9"  and 
the  inside  diameter  7",  what  is  the  area  of  one  side  of  the 
ring? 

#=.7854  (D2  -<f2) 

B  =  .7854  (81  -  49)  =  .7854  x  32  =  25.1328  sq.  in.     Ans. 

Angles 

We  make  two  common  uses  of  angles  :  (1)  to  measure  a  cir- 
cular movement,  and  (2)  to  measure  a  difference  in  direction. 
A  circle  contains  360°,  and  the  angles  at  the  center  of  the 
circle  contain  as  many  degrees  as  their  corresponding  arcs  on 
the  circumference. 

Angle  POE  has  as  many  degrees  as  arc  PE. 

A  right  angle  is  measured  by  a  quarter 
of  the  circumference  of  the  circle,  which 
is  90°. 

The  angle  AOG  is  a  right  angle. 

The  angle  AC,  made  with  half  the  cir- 
cumference of  the  circle,  is  a  straight  angle,  and  the  two  right 
angles,  AOG  and  GOC,  which  it  contains,  are  supplementary 
to  each  other.  When  the  sum  of  two  angles  is  equal  to  90°, 
they  are  said  to  be  complementary  angles,  and  one  is  the  com- 
plement of  the  other.  When  the  sum  of  two  angles  equals  180°, 
they  are  supplementary  angles,  and  one  is  said  to  be  the  supple- 
ment of  the  other. 


MENSURATION  67 

The  number  of  degrees  in  an  angle  may  be  measured  by  a 
protractor.     The  distance  around  a  semicircular  protractor  is 


PROTRACTOR  — Semicircular,  having  180°. 

divided  into  180  parts,  each  division  measuring  a  degree.  It 
-is  used  by  placing  the  center  of  the  protractor  on  the  vertex 
and  the  base  of  the  protractor  on  one  side  of  the  angle  to  be 
measured.  Where  the  other  side  of  the  angle  cuts  the  circular 
piece  of  the  protractor,  the  size  of  the  angle  may  be  read  in 
degrees. 

EXAMPLES 

1.  What  is  the  area  of  a   circular   piece  of  velvet  8"  in 
diameter  ? 

2.  What  is  the  distance  around  the  edge  of  a  hat  6"  in 
diameter  ? 

3.  Name  the  complements  of  angles  of  30°,  45°,  65°,  70°, 
85°. 

4.  Name  the  supplements  of  angles  of  55°,  140°,  69°,  98°  44', 
81°  19'. 

5.  What  is  the  diameter  of  a  wheel  that  is  12'  6"  in  circum- 
ference ? 


68          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

6.  What  is  the  area  of  one  side  of  a  flat  iron  ring  14"  inside 
diameter  and  18"  outside  diameter  ? 

7.  The    wheel    of  a  child's   carriage  is  30"  in  diameter. 
What  is  the  length  of  the  rubber  tire  that  fits  it  ? 

8.  How  much  ribbon  is  needed  to  bind  the  edge  of  a  circu- 
lar cloth  that  exactly  covers  the  top  of  a  center  table  28"  in 
diameter  ? 

9.  A  straw  hat  measures  30"  around  the  rim.     What  is 
the  diameter  of  the  hat  ? 

10.  If  a  circular  dining  room  table  measures  12'  6"  in  cir- 
cumference, what  is  the  greatest  distance  across  the  table  ? 

Triangles 

A  triangle  is  a  plane  figure  bounded  by  three  straight  lines. 
Triangles  are  classified  according  to  the  relative  lengths  of 
their  sides  and  the  size  of  their  angles. 

A  triangle  having  equal  sides  is  called  equilateral.  One 
having  two  sides  equal  is  isosceles.  A  triangle  having  no 
sides  equal  is  called  scalene. 

If  the  angles  of  a  triangle  are  equal,  the  triangle  is  equi- 
angular. 

If  one  of  the  angles  of  a  triangle  is  a  right  angle,  the  tri- 
angle is  a  right  triangle.  In  a  right  triangle  the  side  opposite 
the  right  angle  is  called  the  hypotenuse  and  is  the  longest  side. 
The  other  two  sides  of  the  right  triangle  are  the  legs,  and  are 
at  right  angles  to  each  other, 


EQUILATERAL       ISOSCELES  SCALENE  EIGHT 


MENSURATION 


69 


KINDS  OF  TRIANGLES 
Right  Triangles 


In  a  right  triangle  the 
square  of  the  hypotenuse 
equals  the  sum  of  the 
squares  of  the  other  two 
sides  or  legs. 

If  the  length  of  the  hy- 
potenuse and  one  leg  of  a 
right  triangle  is  known, 
the  other  side  may  be 
found  by  squaring  the 
hypotenuse  and  squaring 
the  leg,  and  extracting  the 
square  root  of  their  dif- 
ference. 


EXAMPLE.  —  If  the  hypotenuse  of  a  right  angle  triangle  is 
30"  and  the  base  is  18",  what  is  the  altitude? 


302  =  30  x  30  =  900 

182  =  18  x  18  =  324 

900  —  324  =  576 

V57U  =  24".     Ans. 


J8" 


Areas  of  Triangles 

The  area  of  a  triangle  may  be  found  when  the  length  of  the 
three  sides  is  given  by  adding  the  three  sides  together,  divid- 
ing by  2,  and  subtracting  from  this  sum  each  side  separately. 
Multiply  the  four  results  together  and  find  the  square  root  of 
their  product. 


70          VOCATIONAL   MATHEMATICS  FOR   GIRLS 

EXAMPLE.  —  What  is   the  area  of   a  triangle  whose   sides 
measure  15,  16,  and  17  inches,  respectively  ? 

15 
16 


17  V24  x  9  x8  x7  =  x/12096 

2)48  V12096  =  109.98  sq.  in.    Am. 

24-15=9 
24  -  16  =  8 
24  -  17  =  7 

Area  of  a  Triangle  =  J  5ase  X  Altitude 

EXAMPLE.  —  What  is  the  area  of  a  triangle  whose  base  is 
17"  and  altitude  10"? 


A  =  ~  x  17  x  ;0  =  85  sq.  in.     Ans. 


EXAMPLES 

1.  A  ladder  17  ft.  long  standing  on  level  ground  reached  to 
a  window  12  ft.  from  the  ground.     If  it  is  assumed  that  the 
wall  is  perpendicular,  how  far  is  the  foot  of  the  ladder  from 
the  base  of  the  wall  ? 

2.  Find  the  area  of  a  triangular  piece  of  cloth  having  the 
base  81"  and  the  height  measured  from  the  opposite  angle  56". 

3.  Find  the  length  of   the  hypotenuse  of   a  right  triangle 
with  equal  legs  and  having  an  area  of  280  sq.  in. 

4.  Find  the  length  of  a  side  of  a  right  triangle  with  equal 
legs  and  an  area  of  72  sq.  in. 

5.  Find  the  hypotenuse  of  a  right  triangle  with  a  base  of 
8"  and  the  altitude  of  7". 

6.  What  is  the  area  of  a  triangle  whose  sides  measure  12, 
19,  and  21  inches  ? 

7.  What  is  the  altitude  of  an  isosceles  triangle  having  sides 
8  ft.  long  and  a  base  6  ft.  long  ? 


MENSURATION  71 

Quadrilaterals 

Four-sided  plane  figures  are  called  quadrilaterals.  Among 
them  are  the  trapezoid,  trapezium,  rectangle,  rhombus,  and  rhom- 
boid. 


SQUARE          RECTANGLE  RHOMBOID  RHOMBUS 


TRAPEZIUM  TRAPEZOID  PARALLELOGRAM 

KINDS  OF  QUADRILATERALS 

A  rectangle  is  a  quadrilateral  which  has  its  opposite  sides 
parallel  and  its  angles  right  angles.  Its  area  equals  the  prod- 
uct of  its  base  and  altitude. 

A=ba 

A  trapezoid  is  a  quadrilateral  having  only  two  sides  parallel. 
Its  area  is  equal  to  the  product  of  the  altitude  by  one  half  the 
sum  of  the  bases. 


In  this  formula    c  =  length  of  longest  side  I 

b  =  length  of  shortest  side 


a  =  altitude 


A  trapezium  is  a  four-sided  figure  with  no  two  sides  parallel. 
The  area  of  a  trapezium  is  found  by  dividing  the  trapezium 
into  triangles  by  means  of  a  diagonal.  Then  the  area  may  be 
found  if  the  diagonal  and  perpendicular  heights  of  the  triangles 
are  known. 


72          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

EXAMPLE.  —  In  the  trapezium  ABCD  if  the  diagonal  is  43' 
and  the  perpendiculars  11'  and  17',  respectively,  what  is  the 
area  of  the  trapezium  ? 

43  X  V-  =^p  =  236i  sq.  ft.,  area  of  ABC 
43  X  -V-  =  ^MH-=365|  sq.  ft.,  area  of  ADC 
602    sq.  ft.,  total  area 
Ans. 

To  find   the   areas   of  irregular  figures, 
draw  the  longest  diagonal  and  upon  this 
diagonal  drop  perpendiculars  from  the  ver- 
tices of  the  figure.     These  perpendiculars  will  form  trapezoids 
and  right  triangles  whose  areas  may  be  determined  by  the  pre- 
ceding rules.     The  sum  of  the  areas  of  the  separate  figures  will 
give  the  area  of  the  whole  irregular  figure. 

Polygons 

A  plane  figure  bounded  by  straight  lines  is  a  polygon.  A 
polygon  which  has  equal  sides  and  equal  angles  is  a  regular 
polygon. 

The  apothem  of  a  regular  polygon  is  the  line  drawn  from  the 
center  of  the  polygon  perpen- 
dicular to  one  of  the  sides. 

A    five-sided    polygon    is    a 
pentagon. 

A    six-sided    polygon    is    a 

PENTAGON  HEXAGON 

hexagon. 

An  eight-sided  polygon  is  an  octagon. 

The  shortest  distance  between  the  opposite  sides  of  a  regu- 
lar hexagon  is  the  perpendicular  distance  between  them,  and 
is  equal  to  the  diameter  of  the  inscribed  circle. 

The  diameter  of  the  circumscribed  circle  is  the  long  diame- 
ter of  a  regular  hexagon. 

The  perimeter  of  a  polygon  is  the  sum  of  all  its  sides. 


MENSURATION  73 

The  area  of  a  regular  polygon  equals  one  half  the  product  of 
the  apothem  and  the  perimeter. 

Formula  ^  —  \  aP 

In  this  formula  P  =  perimeter 

a  =  apothem 

Ellipse 

Only  the  approximate  circumference  of  an  ellipse  can  be  ob- 
tained. 

The  circumference  of  an  ellipse  equals  one  half  the  product  of 
the  sum  of  two  diameters  and  TT. 

If  ^  =  major  diameter 

d2  =  minor  diameter 
C  =  circumference 

then  C-  =  ^±4, 


The  area  of  an  ellipse  is  equal  to  one  fourth  the  product  of 
the  major  and  minor  diameters  by  TT. 

If  A  =  area 

dl  =  major  diameter 
d2  =  minor  diameter 

then  A  =  w^ 

4 

EXAMPLES 

1.  Find  the  area  of  a  trapezium  if  the  diagonal  is  93'  and 
the  perpendiculars  are  19'  and  33'. 

2.  What  is  the  area  of  a  trapezoid  whose  parallel  sides  are 
18  ft.  and  12  ft.,  and  the  altitude  8  ft.  ? 

3.  What  is  the   distance   around   an   ellipse  whose   major 
diameter  is  14"  and  minor  diameter  8"  ? 


74          VOCATIONAL  MATHEMATICS   FOR   GIRLS 

4.  In  the  map  of  a  country  a  district  is  found  to  have  two 
of  its  boundaries  approximately  parallel  and  equal  to  276  and 
216  miles.     If  the  breadth  is  100  miles,  what  is  its  area  ? 

5.  If  the  greater  and  lesser  diameters  of  an  elliptical  man- 
hole door  are  2'  9"  and  2'  6",  what  is  its  area  ? 

6.  Find  the  area  of  a  trapezium  if  the  diagonal  is  78"  and 
the  perpendiculars  18"  and  27". 

7.  The  greater  diameter  of  an  elliptical  funnel  is  4  ft.  6  in., 
and  the  lesser  diameter  is  4  ft.     What  is  its  area  ? 

8.  Find  the  perimeter  of  a  hexagon  having  each  side  15" 
long. 

9.  What  is  the  area  of  a  pentagon  whose  apothem  is  4y 
and  whose  side  is  5"  ? 

Volumes 

The  volume  of  a  rectangular-shaped  bar  is  found  by  multi- 
plying the  area  of  the  base  by  the  length.  If  the  area  is  in 
square  inches,  the  length  must  be  in  inches. 

The  volume  of  a  cube  is  equal  to  the  cube  of  an  edge. 

The  contents  or  volume  of  a  cylindrical  solid  is  equal  to  the 
product  of  the  area  of  the  base  by  the  height. 

If  S  =  contents  or  capacity  of  cylinder 

R  =  radius  of  base 
H  =  height  of  cylinder 
TT  =  3.1416+  or  2f.  (approx.) 

8  = 


EXAMPLE.  —  Find  the  contents  of  a  cylindrical  tank  whose 
inside  diameter  is  14"  and  height  6'. 


H=  6'  =  72" 

8  =  ^  x  7  x  7  x  72  =  11,088  cu.  in. 


MENSURATION 


75 


The  Pyramid 

The  volume  of  a  pyramid  equals  one 
third  of  the  product  of  the  area  of  the  base 
and  the  altitude. 


The  volume  of  a  frustum  of  a  pyramid 
equals  the  product  of  one  third  the  alti- 
tude and  the  sum  of  the  two  bases  and  the 
square  root  of  the  product  of  the  bases. 


The  surface  of  a  regular  pyramid  is  equal  to  the  product  of 
the  perimeter  of  the  bases  and  one  half  the  slant  height. 

S  =  P  X  i  8/1 

The  Cone 

A  cone  is  a  solid  generated  by  a  right  triangle  revolving  on 
one  of  its  legs  as  an  axis. 

The  altitude  of  the  cone  is  the  perpendicular  distance  from 
the  base  to  the  apex. 

The  volume  of  a  cone  equals  the  product  of  the  area  of  the 

base  and  one  third  of  the  altitude. 

F 


or 


V=  .2618 


EXAMPLE.  —  What  is  the  volume  of  a  cone  1-J-"    $ 
in  diameter  and  4"  high  ? 

Area  of  base  =  .  7854  x  f 


7.0686 


=  1.7671  sq.  in. 


=  .2618  x  |  x  4  =  2.3562  cu.  in.    Ans. 

The  lateral  surface  of  a  cone  equals  one  half  the  product  of 
the  perimeter  of  the  base  by  the  slant  height. 


76 


VOCATIONAL  MATHEMATICS   FOR   GIRLS 


EXAMPLE.  —  What  is  the  surface  of  a  cone  having  a  slant 
height  of  36  in.,  and  a  diameter  of  14  in.  ? 


C  =  irD  =  14  X 
44  x  36 


— .  4.4  tf 
=  792  sq.  in.    Ans. 


Frustum  of  a  Cone 

The  frustum  of  a  cone  is  the  part  of  a  cone  included  between 
the  base  and  a  plane  or  upper  base  which  is  parallel  to  the 
lower  base. 

The  volume  of  a  frustum  of  a  cone  equals  the  product  of  one 
third  of  the  altitude  and  the  sum  of  the  two  bases  and  the 
square  root  of  their  product. 

When  H  =  altitude 

Bl  ==  upper  base 
R  =  lower  base 
V=±H(B  +  1?  +  VB&) 

The  lateral  surface  of  a  frustum  of  a  cone  equals  one  half  the 
product  of  the  slant  height  and  the  sum  of  the  perimeters 
of  the  bases. 

The  Sphere 

The  volume  of  a  sphere  is  equal  to 


where  R  is  the  radius. 

The  surface  of  a  sphere  is  equal  to 


The  Barrel 

To  find  the  cubical  contents  of  a  barrel,  (1)  multiply  the 
square  of  the  largest  diameter  by  2,  (2)  add  to  this  product 


MENSURATION  77 

the  square  of  the  head  diameter,  and  (3)  multiply  this  sum  by 
the  length  of  the  barrel  and  that  product  by  .2618. 

EXAMPLE.  —  Find  the  cubical  contents  of  a  barrel  whose 
largest  diameter  is  21"  and  head  diameter  18",  and  whose 
length  is  33". 

212  =  441  x  2  =  882  V=  [(Z>2  x  2)  +  d2]  x  L  x  .2618 
182  =  324              324  39798 

120(3  .2618 

33  10419-11  cu.  in. 

=  45.10  gal.  Ans. 


3618 

3618  10419.11 

39798  231 


Similar  Figures 

Similar  figures  are  figures  that  have  exactly  the  same  shape. 
The  areas  of  similar  figures  have   the    same   ratio   as  the 
squares  of  their  corresponding  dimensions. 

EXAMPLE.  —  If  two  boilers  are  15'  and  20'  in  length,  what  is 
the  ratio  of  their  surfaces  ? 

|jj.  =  f,  ratio  of  lengths 

§!  =  JL    ratio  of  surfaces 
4'2      16 

One  boiler  is  T9^  as  large  as  the  other.    Ans. 

The  volumes  of  similar  figures  are  to  each  other  as  the  cubes 
of  their  corresponding  dimensions. 

EXAMPLE.  —  If  tw°  iron  balls  have  8"  and  12"  diameters, 
respectively,  what  is  the  ratio  of  their  volumes  ? 

r8^  =  |,  ratio  of  diameters 

=  28T,  ratio  of  their  volumes.     Ans. 

One  ball  weighs  $7  as  much  as  the  other. 


78          VOCATIONAL  MATHEMATICS  FOR   GIRLS 

EXAMPLES 

1.  Find  the  volume  of  a  rectangular  box  with  the  following 
inside  dimensions  :  8"  by  10"  and  4'  long. 

2.  The  radius  of  the  small  end  of  a  bucket  is  4  in.     Water 
stands  in  the  bucket  to  a  depth  of  9  in.,  and  the  radius  of  the 
surface  of  the  water  is  6  in.     (1)    Find  the  volume  of  the  water 
in  cubic  inches.     (2)    Find  the  volume  of  the  water  in  gallons 
if  a  cubic  foot  contains  7.48  gal. 

3.  What  is  the  volume  of  a  steel  cone  2^"  in  diameter  and 
6"  high? 

4.  Find  the  contents  of  a  barrel  whose  largest  diameter  is 
22",  head  diameter  IS",  and  height  35". 

5.  What  is  the  volume  of  a  sphere  8"  in  diameter  ? 

6.  What  is  the  volume  of  a  pyramid  with  a  square  base, 
4"  on  a  side  and  11"  high  ? 

7.  What  is  the  surface  of  a  wooden  cone  with  a  6"  diameter 
and  14"  slant  height  ? 

8.  Find  the  surface  of  a  pyramid  with  a  perimeter  of  18" 
and  a  slant  height  of  11". 

9.  Find  the  volume  of  a  cask  whose  height  is  3^'  and  the 
greatest  radius  16",  and  the  least  radius  12",  respectively. 

10.  How  many  gallons  of  water  will  a  round  tank  hold  which 
is  4  ft.  in  diameter  at  the  top,  5  ft.  in  diameter  at  the  bottom, 
and  8  ft.  deep  ?     (231  cu.  in.  =  1  gal.) 

11.  What  is  the  volume   of  a  cylindrical  ring  having  an 
outside  diameter  of  6-J-",  an  inside  diameter  of  5Ty,  and  a 
height  of  3f "  ?     What  is  its  outside  area  ? 

12.  If  9  tons  of  wild  hay  occupy  a  cube  7'  x  1'  X  7',  how 
many  cubic  feet  in  one  ton  of  hay  ? 

13.  A  sphere  has  a  circumference  of  8.2467".     (a)  What  is 
its  area  ?     (6)  What  is  its  volume  ? 


MENSURATION  79 

14.  If  it  is  desired  to  make  a  conical  can  with  a  base  3.5"  in 
diameter  to  contain  1  pint,  what  must  the  height  be  ? 

15.  What  is  the  area  of  one  side  of  a  flat  ring  if  the  inside 
diameter  is  2£' '  and  the  outside  diameter  4£"  ? 

16.  There  are  two  balls  of  the  same  material  with  diameters 
4"  and  V,  respectively.     If  the  smaller  one  weighs  3  lb.,  how 
much  does  the  larger  one  weigh  ? 

17.  If  the  inside  diameter  of  a  ring  is  5  in. ,  what  must  the 
outside  diameter  be  if  the  area  of  the  ring  is  6.9  sq.  in.  ? 

18.  How  much  less  paint  will  it  take  to  paint  a  wooden  ball 
4"  in  diameter  than  one  10"  in  diameter  ? 

19.  What  is  the  weight  of  a  brass  ball  3£"  in  diameter  if 
brass  weighs  .303  lb.  per  cubic  inch  ? 

20.  A  cube  is  19"  011  its  edge,      (a)  Find  its  total  area. 
(&)  Its  volume. 

21.  If  a  barrel  of  water  contains  about  4  cu.  ft.,  what  is 
the  approximate  weight  of  the  barrel  of  water?      (1  cu.  ft. 
of  water  weighs  62.5  lb.) 

22.  A  conical  funnel  has  an  inside  diameter  of  19.25"  at  the 
base  and  is  43"  high  inside,     (a)  Find  its  total  area,     (b)  Find 
its  cubical  contents. 

23.  A  pointed  heap  of  corn  is  in  the  shape  of  a  cone.     How 
many  bushels  in  a  heap  10'  high,  with  a  base  20'  in  diameter  ? 
A  bushel  contains  2150.42  cu.  in. 

24.  Find  the  capacity  of  a  rectangular  bin  6  ft.  wide,  5  ft. 
6  in.  deep,  and  8  ft.  3  in.  long. 

25.  Find  the  capacity  of  a  berry  box  with  sloping  sides  5.1" 
by  5.1"  on  top,  4.3"  by  4.3"  at  the  bottom,  and  2.9"  in  depth. 

26.  Find   the    capacity   of   a    cylindrical    measure    13"   in 
diameter  and  6"  deep. 

27.  How  many  tons  of  nut  coal  are  in  a  bin  5  ft.  wide  and 
8  ft.  long  if  filled  evenly  to  a  depth  of  4  ft.  ?     Average  nut  coal 
weighs  52  lb.  to  a  cubic  foot. 


CHAPTER    III 
INTERPRETATION  OF  RESULTS 

Reading  a  Blue  Print.  —  Everyone  should  know  how  to  read 
a  blue  print,  which  is  the  name  given  to  working  plans  and 
drawings  with  white  lines  upon  a  blue  background.  The  blue 
print  is  the  language  which  the  architect  uses  to  the  builder, 
the  machinist  to  the  pattern  maker,  the  engineer  to  the  foreman 


EXTERIOR  VIEW  OF  COMPLETED  HOUSE 

of  construction,  and  the  designer  to  the  workman.  Through 
following  the  directions  of  the  blue  print  the  carpenter,  metal 
worker,  and  mechanic  are  able  to  produce  the  object  wanted 
by  the  employer  and  his  designer  or  draftsman. 

Blue  Print  of  a  House.  —  An  architect,  in  drawing  the  plans 
of  a  house,  usually  represents  the  following  views :  the  ex- 
terior views  to  show  the  appearance  of  the  house  when  it  is 
finished  j  views  of  each  floor,  including  the  basement,  to  show 

80 


INTERPRETATION   OF  RESULTS 


81 


WEST  ELEVATION  OF  HOUSE 


j. i     i :    : -___ 

EAST  ELEVATION 


the  location  of  rooms,  windows,  doors,  and  stairs.  Detailed 
plans  of  sections  are  drawn  for  the  contractors  to  show  the 
method  of  construction. 


82         VOCATIONAL  MATHEMATICS  FOR   GIRLS 


NORTH  ELEVATION 


!  — '  ' 

•*'—-*[     —      —      —-.--——         -      —     —  —     —     — .  ,  _;_ 

A—  -——'  —  —    —  —  -— £a  rt  ft  fro  rn 

SOUTH  ELEVATION 


Pupils  should  be  able  to  form  a  mental  picture  of  the  appear- 
ance of  a  building  constructed  from  any  blue  print  plan  set 
before  them.  They  should  have  practice  in  reading  the  plans 
of  the  house  and  in  computing  the  size  of  the  rooms  directly 
from  the  blue  print. 


INTERPRETATION   OF  RESULTS 

-FfagsloncCap 


83 


1.  What  is  the  height  of  the  rooms  on  the  first  floor  ? 

2.  What  is  the  height  of  the  rooms  on  the  second  floor  ? 

3.  What  is  the  height  of  the  cellar,  first,  and  second  floors  ? 


EC. 


GROUND  FLOOR  PLAN 


84 


VOCATIONAL  MATHEMATICS  FOR   GIRLS 


1.  What  is  the  frontage  of  the  house  ? 

2.  What  is  the  depth  of  the  house  ? 

3.  What  is  the  length  and  width  of  the  front  porch  ? 

4.  What  is  the  length  and  width  of  the  living  room  ?   the 
dining  room  ?  the  kitchen  ? 


SECOND  FLOOR  PLAN 

1.  What  is  the  size  of  each  of  the  bedrooms  ?     (Compute 
with  aid  of  ground  floor  plan.) 

2.  What  are  the  dimensions  of  the  bathroom  ? 

3.  How  large  is  the  storage  room  ? 

Two  views  are  usually  necessary  in  every  working  drawing, 
one  the  plan  or  top  view  obtained  by  looking  down  upon  the 
object,  and  the  other  the  elevation  or  front  view.  When  an 


INTERPRETATION   OF  RESULTS  85 

object   is  very  complicated,  a   third  view,  called   an   end   or 
profile  view  is  shown. 

All  the  information,  such  as  dimensions,  etc.,  necessary  to  construct 
whatever  is  represented  by  the  blue  print  must  be  supplied  on  the  draw- 
ing. If  the  blue  print  represents  a  machine,  it  is  necessary  to  show  all 
the  parts  of  the  machine  put  together  in  their  proper  places.  This  is 
called  an  assembly  drawing.  Then  there  must  be  a  drawing  for  each 
part  of  the  building  or  the  machine,  giving  information  as  to  the  size, 
shape,  and  number  of  the  pieces.  Then  if  there  are  interior  sections, 
these  must  be  represented  in  section  drawings. 

Drawing  to  Scale.  —  As  it  is  impossible  to  draw  most  objects 
full  size  on  paper,  it  is  necessary  to  make  the  drawings  pro- 
portionately smaller.  This  is  done  by  making  all  the  dimen- 
sions of  the  drawing  a  certain  fraction  of  the  true  dimensions 
of  the  object.  A  drawing  made  in  this  way  is  said  to  be  drawn 
to  scale. 


TRIANGULAR  SCALE 

The  dimensions  on  the  drawing  designate  the  actual  size  of 
the  object  —  not  of  the  drawing.  If  a  drawing  were  made  of 
an  iron  door  25  inches  long,  it  would  be  inconvenient  to  repre- 
sent the  actual  size  of  the  door,  and  the  drawing  might  be  made 
half  or  quarter  the  size  of  the  door,  but  on  the  drawing  the 
length  would  read  25  inches. 

In  making  a  drawing  "  to  scale,"  it  becomes  very  tedious  to 
be  obliged  to  calculate  all  the  small  dimensions.  In  order  to 
obviate  this  work  a  triangular  scale  is  used.  It  is  a  rule  with 
the  different  scales  marked  on  it.  By  practice  the  student  will 
be  able  to  use  the  scale  with  as  much  ease  as  the  ordinary 
rule. 

QUESTIONS   AND   EXAMPLES 

1.  Tell  what  is  the  scale  and  the  length  of  the  drawing  of 
each  of  the  following : 


86         VOCATIONAL  MATHEMATICS  FOR  GIRLS 

a.  An  object  14"  long  drawn  half  size. 

b.  An  object  2.6"  long  drawn  quarter  size. 

c.  An  object  34"  long  drawn  one  third  size. 

d.  An  object  41"  long  drawn  one  twelfth  size. 

2.  If  a  drawing  made  to  the  scale  of  f  "  =  1  ft.  is  reduced 
i  in  size,  what  will  the  new  scale  be  ? 

3.  A  drawing  is  made  -^  size.     If  the  scale  is  doubled,  how 
many  inches  to  the  foot  will  the  new  scale  be  ? 

4.  On  the  TJg"  scale,  how  many  feet  are  there  in  18  inches  ? 

5.  On. the  y  scale,  how  many  feet  are  there  in  26  inches  ? 

6.  On  the  \"  scale,  how  many  feet  are  there  in  27  inches  ? 

7.  If  the  drawing  of  a  door  is  made  ^  size  and  the  length  of 
the  drawing  is  8^",  what  will  it  measure  if  made  to  scale  3" 
=  1  f  t.  ? 

8.  What  will  be  the  dimensions  of  the  drawing  of  a  banquet 
hall  582'  by  195'  if  it  is  made  to  a  scale  of  Ty '  =  1  ft.  ? 

Estimating  Distances.  —  Everyone  meets  occasions  in  daily 
life  when  it  is  of  utmost  importance  that  distance  or  weight 
should  be  correctly  estimated. 

Few  people  have  a  clear  conception  of  even  our  common  standards  of 
measurements.  This  is  due  to  the  fact  that  the  average  person  has  never 
given  the  proper  attention  to  them.  Improvement  will  be  noticed  after  a 
small  amount  of  drill.  To  illustrate  :  if  the  distances  of  one  inch,  one 
foot,  one  yard,  six  feet,  and  ten  feet  are  measured  off  in  a  classroom  so 
that  an  actual  view  of  standard  distances  is  obtained,  and  then  pupils  are 
asked  to  estimate  other  and  unknown  distances,  they  will  estimate  with  a 
greater  degree  of  accuracy.  Pupils  should  be  able  to  estimate  within 
^  inch  any  distance  up  to  a  yard. 

The  power  of  estimating  longer  distances,  such  as  the  distance  between 
buildings,  across  streets,  or  between  streets,  may  be  developed  by  laying 
off  on  a  straight  road  one  hundred  feet,  three  hundred  feet,  and  five  hun- 
dred feet  sections,  with  the  proper  distance  marked  on  each. 

The  same  plan  applies  to  heights  of  buildings,  etc.  Standards  of  alti- 
tude may  thus  be  established. 

Pupils  should  measure  in  their  homes  pieces  of  furniture  and  wall 
openings  so  that  they  may  develop  an  eye  for  estimating  distances. 


INTERPRETATION   OF  RESULTS  87 

1.  Estimate  the  length  and  width  of  the  schoolroom.    Verify 
this  estimate  by  actual  measurement  and  express  the  accuracy 
of  your  estimate  in  per  cent. 

2.  Estimate  the  height  and  width  of  the  school  door.    Verify 
this  estimate  by  actual  measurement  and  express  the  accuracy 
of  the  estimate  in  per  cent. 

3.  Estimate  the  width  and  length  of  the  window  panes ; 
the  width  and  length  of  the  window  sill. 

Estimating  Weights.  —  What  is  true  concerning  the  advan- 
tage of  being  able  to  estimate  distances  applies  equally  well  to 
weights. 

In  this,  guesswork  may  be  largely  eliminated.  A  little  mental  figur- 
ing on  the  part  of  the  pupil  will  usually  produce  clear  results.  Weight 
depends  not  only  on  volume  but  also  on  the  density  of  the  material. 
Regular  blocks  of  wood  are  excellent  to  begin  with,  and  later  small 
spheres  and  rectangular  blocks  of  different  metals  afford  good  material. 

1.  Select  blocks  of  wood,  coal,  iron,  lead,  tin,  or  copper,  and 
estimate  their  respective  weights. 

2.  Estimate  the  weight  of  a  chair. 

3.  Estimate  the  weight  of  different  persons. 

Methods  of  Solving  Examples.  —  Every  commercial,  household, 
or  mechanical  problem  or  operation  has  two  distinct  sides  :  the 
collecting  of  data,  and  the  solving  of  the  problem. 

The  first  part,  the  collecting  of  data,  demands  a  knowledge 
of  the  materials  and  conditions  under  which  the  problem  is 
given,  and  calls  for  the  exercise  of  judgment  as  to  the  neces- 
sary accuracy  of  the  work. 

There  are  three  ways  by  which  a  problem  may  be  solved : 

1.  Exact  method. 

2.  Rule  of  thumb  method,  by  the  use  of  a  formula  or  a  rule 
committed  to  memory. 

3.  By  means  of  tables. 

The  exact  method  of  solving  a  problem  in  arithmetic  is  the 
one  usually  taught  in  school  and  is  the  method  obtained  by 


88         VOCATIONAL  MATHEMATICS  FOR  GIRLS 

analysis.  Everyone  should  be  able  to  solve  a  problem  by  the 
exact  method. 

The  Rule  of  Thumb  Method.  —  Many  of  the  problems  that 
arise  in  home,  office,  and  industrial  life  have  been  met  before, 
and  very  careful  judgment  has  been  exercised  in  solving  them. 
As  the  result  of  this  experience  and  the  tendency  to  abbreviate 
and  devise  shorter  methods  that  give '  sufficiently  accurate  re- 
sults, we  find  many  rule  of  thumb  methods  used  by  the  house- 
wife, the  storekeeper,  the  nurse,  etc.  The  exact  method  would 
require  considerable  time  and  the  use  of  pencil  and  paper, 
whereas  in  cases  that  are  not  too  complicated  the  estimates, 
based  on  experience  or  rule,  give  a  quick  and  accurate  result. 

In  solving  problems  involving  the  addition  and  subtraction 
of  fractions,  use  the  yardstick  or  tape  to  carry  on  the  compu- 
tation. To  illustrate :  if  we  desire  to  add  1  and  J-  of  a  yard, 
place  the  thumb  over  1  of  a  yard  divisions,  then  slide  (move)  the 
thumb  along  the  divisions  corresponding  to  J-  of  a  yard,  and 
then  read  the  number  of  divisions  passed  over  by  the  thumb. 
In  this  case  the  result  is  21  inches. 

The  Use  of  Tables.  —  In  the  commercial  world  the  tendency 
is  to  do  everything  in  the  quickest  and  the  most  economical 
way.  To  illustrate :  hand  labor  is  more  costly  than  machine 
work,  so,  whenever  possible,  machine  work  is  substituted  for 
hand  labor.  The  same  tendency  applies  to  calculations  in  the 
dressmaking  shop  or  the  office.  The  exact  methods  of  doing 
examples  are  not  the  quickest,  nor  are  they  more  easily  under- 
stood and  performed  by  the  ordinary  girl  than  the  shorter 
methods.  Since  a  great  many  of  the  problems  in  calculation 
that  arise  in  the  daily  experiences  of  the  office  assistant,  the 
housewife,  the  dressmaker,  the  nurse,  etc.  are  about  ordinary 
things  and  repeat  themselves  often,  it  is  not  necessary  to  work 
them  anew  each  time,  if,  when  they  are  once  solved,  results  are 
kept  on  file  in  the  form  of  tables. 

See  pages  220,  222,  and  254  for  tables  used  in  this  book. 


PART   II  — PROBLEMS   IN   HOMEMAKING 

CHAPTER   IV 
THE  DISTRIBUTION  OF  INCOME 

THE  economic  standing  of  every  person  in  the  community 
depends  upon  three  things :  (1)  earning  capacity,  (2)  spend- 
ing ability,  and  (3)  the  saving  habit.  The  first  regulates  the 
amount  of  income ;  the  second  determines  the  purchasing 
power  after  the  amount  is  earned ;  the  third  paves  the  way 
to  independence. 

The  welfare  of  every  person,  whether  single  or  married, 
depends  upon  the  systematic  and  careful  regulation  of  each 
of  these  three  items.  No  matter  how  large  or  small  his  wages 
or  salary,  if  he  does  not  spend  his  money  wisely  and  carefully, 
or  save  each  week  or  month  a  certain  per  cent  of  his  earnings, 
a  young  man  or  woman  is  not  likely  to  make  a  success  of  life. 

A  young  woman  usually  has  more  to  do  with  the  spending  of  money 
than  a  young  man.  The  wife  is  really  the  spender  and  the  husband  the 
earner  in  the  ordinary  home.  Therefore,  it  becomes  necessary  for  every 
young  woman  to  know  how  to  get  one  hundred  cents  out  of  a  dollar.  In 
order  to  do  this,  she  must  know  how  to  distribute  the  income  over  such 
items  as  rent,  food,  clothing,  incidental  expenses  due  to  sickness,  pleas- 
ure, or  self-improvement.  The  proportion  spent  for  each  item  should  be 
carefully  regulated. 

Incomes  of  American  Families 

The  average  family  income  of  both  foreign  and  native  born  heads  is 
about  $  725  a  year  ;  that  of  families  with  native  born  heads  alone  is 
about  $  800.  Not  more  than  one-fourth  have  incomes  exceeding  $  1000. 
The  daily  wages  of  adult  men  range  from  $  1.50  to  $  5.00.  This  amounts 
on  the  average  from  .$450  to  $1500  a  year. 

The  family,  the  head  of  which  earns  only  a  few  hundred  dollars  a 
year,  must  either  be  contented  with  comparatively  low  standards  of  liv- 

89 


90 


VOCATIONAL  MATHEMATICS  FOR   GIRLS 


ing  or  obtain  additional  income,  either  through  the  labor  of  children  or 
from  boarders  or  lodgers.  The  foreign-born  workers  resort  to  the  labor 
of  children  and  mothers  more  than  do  the  native  Americans.  The  second 
course  is  quite  often  adopted  so  that  the  average  income  of  workingmen's 
families  is  considerably  greater  than  the  average  earnings  of  the  heads  of 
the  families. 


INCOMES 


EXPENDITURES 


Based  on  Statistics  of  Twenty-five  Thousand  Families  with  an  Average 
Yearly  Income  of  Seven  Hundred  and  Fifty  Dollars 

EXAMPLES 

1.  The  average  workingman's  family  spends  at  least  two- 
fifths  of  its  income  for  food.     What  per  cent  is  spent  for  food  ? 

2.  If  the  income  of  a  workingman's  family  is  $  800,  and  the 
amount  spent  for  food  is  $  350,  what  per  cent  is  spent  for  food  ? 

3.  One-fifth  of  the  expenditure  of  workingmen's  families  is 
for  rent.     What  per  cent  ? 

4.  A   family  with  an   income   of    $  800   spends    $  12.50   a 
month  for  rent.     What  per  cent  of   the  income  is  spent  for 
rent?     Is  this  too  much? 

5.  A  family's  income  is  $  760.    The  father  contributes  $  601. 
What  per  cent  of  the  income  is  contributed  by  the  father  ? 

6.  A  family  of  six  has  an  income  of   $  840.     The   father 
contributes    $  592,  mother  $  112,  and  one  child  the  balance. 
What  per  cent  is  contributed  by  the  mother  and  child? 


THE   DISTRIBUTION   OF   INCOME  91 

7.  A  man  and  wife  have  an  income  of  $  971.  The  husband 
earns  $  514,  the  wife  keeps  boarders  and  lodgers,  and  provides 
the  rest  of  the  income.  What  per  cent  of  the  income  is  con- 
tributed by  the  boarders  and  lodgers  ? 

Cost  of  Subsistence 

Shelter,  warmth,  and  food  demand  from  two-thirds  to  three- 
fourths  of  the  income  of  most  workingmen's  families.  This 
leaves  for  everything  else  —  clothing,  furniture,  sickness,  death, 
insurance,  religion,  education,  amusements,  savings  —  only  one- 
third  or  one-fourth  of  the  income.  Between  $  200  and  $  250  a 
year  may  be  considered  the  usual  outlay  of  workingmen's  fami- 
lies for  all  these  purposes  combined.  It  is  in  these  respects 
that  the  greatest  difference  appears  between  the  families  of 
the  comparatively  poor  and  the  families  of  the  well-to-do.  -  The 
well-to-do  spend  not  only  more  in  absolute  amount,  but  also  a 
larger  proportion  of  their  incomes  on  these,  in  general,  less 
absolutely  necessary  things. 

Clothes.  —  On  the  average,  approximately  one-eighth  of  the 
income  in  workingmen's  families  goes  for  clothes.  To  those 
who  keep  abreast  of  the  fashions  and  who  dress  with  some 
elegance,  it  may  seem  quite  preposterous  that  a  family  of  five 
should  spend  only  $  100  or  less  a  year  for  clothing,  but  multi- 
tudes of  working-class  families  are  clad  with  warmth  and  with 
decency  on  such  an  expenditure. 

EXAMPLES 

1.  If  two-thirds    of   the   average  workingman's   income   is 
spent  for  shelter,  warmth,  and  food,  what  per  cent  is  used  ? 

2.  A  family,  receiving  an  income  of  $  847,  spends  $  579  for 
shelter,  warmth,  and  food.     What  per  cent  is  used  ? 

3.  If  one-eighth  of  the  income  of  the  average  workingmen's 
family  is  spent  for  clothes,  what  is  the  per  cent  ? 

4.  A  family  receives  an  income  of  $  768,  and  $  94  is  spent 
for  clothes.     What  per  cent  is  spent  for  clothes  ? 


92         VOCATIONAL  MATHEMATICS  FOR   GIRLS 

The  High  Cost  of  Living 

The  average  cost  of  living  represents  the  amount  that  must 
be  expended  during  a  given  period  by  the  average  family 
depending  on  an  average  income.  The  maximum  or  minimum 
cost,  however,  is  another  phase  of  the  problem.  It  no  longer 
involves  the  amount  of  dollars  and  cents  necessary  to  buy 
and  pay  for  life's  necessaries,  but  involves  questions  of  home 
management  and  housekeeping  skill,  which  cannot  be  stand- 
ardized. About  1907  food  and  other  necessities  of  life  began 
to  increase  in  cost  —  and  this  has  continued  to  the  present  day. 

EXAMPLES 

1.  In  1906  a  ton  of  stove  coal  cost  $  5.75,  and  in  1915  $  8.75. 
What  was  the  per  cent  of  increase  in  the  cost  of  coal  ? 

2.  In  1907  a  suit  of  clothes  cost  $15.     The  same  suit  in 
1912  cost  $  19.75.     What  was  the  per  cent  of  increase  ? 

3.  In  1908  a  barrel  of  flour  cost  $  6.10.     The  same  barrel  of 
flour  cost  in  1914  $  8.25.     What  was  the  per  cent  of  increase  ? 

Division  of  Income 

A  girl  should  always  consider  her  income  for  the  entire  year 
and  divide  it  with  some  idea  of  time  and  relative  proportion. 
If  she  earns  a  good  salary  for  only  ten  months  of, the  year, 
she  must  save  enough  during  those  months  to  tide  her  over  the 
other  two.  For  instance,  if  a  teacher  earns  $  60  a  month  for 
10  months  of  the  year,  her  actual  monthly  income  is  $  50. 
The  milliner,  the  trained  nurse,  the  actress,  and  sometimes  even 
the  girl  working  in  the  mill  have  the  same  problem  to  confront. 

No  girl  has  a  right  to  spend  nearly  all  she  earns  on  clothing, 
neither  should  she  spend  too  much  for  amusement.  We  find 
from  investigations  that  have  been  made  that  girls  earning  $  8 
or  $  10  a  week  usually  spend  about  half  their  income  on  board 
and  laundry.  Girls  earning  a  larger  income  may  pay  more 
for  board,  but  not  quite  so  great  a  fractional  part.  In  these 


THE   DISTRIBUTION   OF   INCOME  93 

days,  when  the  cost  of  living  is  so'  high,  a  girl  should  consider 
carefully  a  position  that  includes  her  board  and  laundry,  for  in 
such  a  position  she  will  be  better  off  financially  at  the  end 
of  the  year  than  her  higher  salaried  sister,  who  has  to  pay 
for  the  cost  of  her  own  living.  The  housegirl  can  save  about 
twice  as  much  as  the  average  stenographer. 

We  find  that  the  average  girl  needs  to  spend  about  one-fifth 
of  her  income  for  clothing.  A  poor  manager  will  often  spend 
as  much  as  one-third  and  not  be  very  well  dressed  at  that, 
because  she  buys  cheap  materials,  that  have  to  be  frequently 
replaced,  and  follows  every  passing  fad  and  style.  Choose 
medium,  styles  and  good  materials  and  you  will  look  more 
richly  dressed.  Keep  the  shoes  shined,  straight  at  the  heel, 
and  the  strings  fresh.  Keep  gloves  mended,  and  as  clean  as 
possible.  If  you  spend  more  on  clothing  than  the  allotted  one- 
fifth,  you  will  have  to  go  without  something  else.  It  may  be 
spending  money,  or  it  may  be  gift  or  charity  money,  and  quite 
often  it  is  the  bank  account  that  suffers. 

Every  person  should  save  some  part  of  his  income.  One 
never  knows  when  sickness,  lack  of  employment,  or  ill  health 
may  come.  Saving  money  is  a  habit  and  one  that  should  be 
acquired  the  very  first  year  that  a  person  earns  his  own  living. 

EXAMPLES 

1.  A  girl  earns  $  12  a  week  for  42  weeks,  and  in  this  time 
spends  $  144  for  clothing.     Is  she  living  within  the  per  cent 
of  her  income  that  should  be  spent  for  clothing  ? 

2.  A  salesgirl  earns  $  8  a  week.     She  spends  $  98  a  year  for 
clothes.     Is  she  living  within  her  income  ? 

3.  A  girl  earns  $  5  a  week  and  pays  half  of  it  to  her  home. 
She  has  two  car  fares  and  a  14-cent  lunch  each  day.    How  much 
should  she  spend  on  clothing  each  year  ?     How  much  has  she 
for  spending  money  each  week  ?    Should  she  save  any  money  ? 

4.  Which  girl  is  the  better  off  financially,  one  earning  $  6 
a  week  as  a  housemaid  or  one  earning  $  7  a  week  in  a  store  ? 


94         VOCATIONAL  MATHEMATICS  FOR   GIRLS 

Buying  Christmas  Gifts 

Let  the  gift  be  something  useful.  Do  not  be  tempted  by  the 
display  of  fancy  Christmas  articles,  for  it  is  on  these  that  the 
merchant  makes  his  profit  for  extra  decorations  and  light. 
Think  of  the  person  for  whom  you  are  buying.  She  may  not 
have  the  same  tastes  as  you  have,  so  give  something  that  she 
will  like  rather  than  something  she  ought  to  like.  For  in- 
stance, a  certain  girl  may  be  very  fond  of  light  hair-ribbons 
when  you  know  that  dark  ones  would  be  much  more  sensible, 
but  at  Christmas  give  the  light  ones. 

The  stores  always  show  an  extra  supply  of  fancy  neckwear. 
A  collar  cannot  be  worn  more  than  three  days  without  becom- 
ing soiled,  so  even  25  cents  is  too  much  to  pay  for  something 
that  cannot  be  cleansed.  Over-trimmed  Dutch  collars  and 
jabots  easily  rip  apart.  Choose  the  plain  ordinary  ones  that 
you  would  be  glad  to  wear  any  day.  You  see  whole  counters 
of  handkerchiefs  displayed  with  embroidery,  lace,  and  ruffles. 
A  linen  handkerchief,  even  of  very  coarse  texture,  is  more 
suitable. 

Be  careful  also  about  bright  colors,  for  everything  about  the 
store  is  so  gay  that  ordinary  things  appear  dull,  but  when 
you  get  them  out  against  the  white  snow,  they  will  be  bright 
enough. 

EXAMPLES 

1.  Shortly  before  Christmas  I   purchased  -J-  doz.  handker- 
chiefs for  $  1.50.     One  month  later  I  purchased  the  same  kind 
of  handkerchiefs  at  16|  cents  each  or  6  for  $  1.00.     What  per 
cent  did  I  save  on  the  second  purchase? 

2.  I  also  bought  a  chiffon  scarf  for  which  I  paid   $2.25. 
Early  in  the  fall  I  saw  similar  scarfs  selling  for  $  1.50.     How 
much  did  I  lose  by  not  making  my  purchase  at  that  time? 
What  per  cent  did  I  lose  ? 

3.  I  bought  at  Christmas  two  pairs    of   silk  stockings  at 
$  1.50  per  pair.     If  I  had  purchased  the  stockings  in  October 


THE   DISTRIBUTION   OF   INCOME 


95 


they  would  have  cost  me  $  1.121  per  pair.      How  much  would 
I  have  saved  ?     What  per  cent  would  I  have  saved  ? 

An  Expense  Account  Book 

Every  person  and  every  family  should  keep  an  expense 
account  showing  each  year's  record  of  receipts  and  expendi- 
tures. A  sample  form  is  shown  in  page  96.  Rule  sheets  in  a 
similar  manner  for  the  solution  of  the  problems  that  follow. 

At  the  end  of  the  year  a  summary  should  be  made  of  receipts  and  dis- 
bursements in  some  such  form  as  the  following  : 


YEARLY   SUMMARY 

Receipts 


Disbursements 


RECEIPTS 

Cash  on  hand  January  1 

Salary,  etc. 

Other  Income 

DISBURSEMENTS 

Savings  and  Insurance 

Rent 

Food 

Clothing 

Laundry 

Car  fares 

Stamps  and  Stationery 

Health 

Recreation 

Education 

Gifts,  Church,  Charity 

Incidentals 

Balance  on  Hand  December  31 

Totals 

. 

Rule  similar  sheets  for  the  solution  of  the  following  problems. 


96 


VOCATIONAL  MATHEMATICS  FOR   GIRLS 


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THE   DISTRIBUTION   OF   INCOME  97 


EXAMPLES 

1.  A  man  and  wife  have  an  income  of  $  1000  a  year.     The 
disbursements  for  the  month  of  October  are  as  follows  : 

Rent,  $  15  Tooth  paste,  $.18 

Telephone,  1.45  Provisions,  5.85 

Repair  on  coat,  5.80  Life  insurance,  7.40 

Gas,  .75  Coal,  7.50 

Dinner,  1.60  Outlook  (1  year),  3.00 

Stationery,  2.51  Assistance,  .60. 

Fares,  .85  Shampoo,  .50 

Groceries,  10.35  Fares,  .60 

Fruit,  .30  Rubbers,  .90 

Theater,  .50  Soap,  .10 

Papers,  .06  Church,  .25 

Church,  .25  Milk,  .56 

Milk,  .71  Ice,  .40 

Ice,  .45  Papers,  .11 

Electricity,  1.00  Vase  for  D.,  .75 

Laundry,  .50  Peroxide,  .25 

Enter  the  above  disbursements  in  the  expense  account  book. 
Find  the  total  amount. 

What  per  cent  was  spent  for  food  ?  house  ?  clothing  ? 
housekeeping  ?  luxuries  ?  savings  ? 

2.  The  items  of  expense  for  the  month  of  January,  1915,  are  : 
rent  and  water,  $  15  ;  operating  expense  :  light  and  heat,  $  11  ; 
food  :  meats,  groceries,  $  30  ;  labor  or  services,  $  16.65 ;  cloth- 
ing,   $  15  ;    physician,    $  1 ;    carfares,   $  2.85 ;    books,    $  1.00  ; 
amusements,   $  4  ;    cigars,   $  1.00  ;    gifts,    $  1.00  ;    sundry  ex- 
penses, $  1.50.     Treat  as  in  Ex.  1. 

3.  A  family  of  two  receives  an  income  of   $  1200  a  year. 
They  spend  per  week  $  6.93  for  food,  $  3.51  for  rent,  $  3.49 
for  operating  expenses,  $  5.81  for  contingency.     What  is  the 
amount    for   each    item    per    month    (4    weeks)  ?    per    year 
(52  weeks)  ?     What  is  the  per  cent  of  each  item  ? 


98          VOCATIONAL   MATHEMATICS   FOR    GIRLS 

4.  A  young  married  woman  has  an  income  of  $  1200  a  year 
—  $  100  a  month.      The   following  represents   the  way  she 
spends  her  income  a  month : 

Savings  bank,  $5.00  Ice  (set  aside  in  the  winter  months 

Kent,  25.00  for  the  summer),  $0.23 

Insurance,  5.00  Necessary  carfares  (the  house   is 

Groceries,  4.70  located  in  the  country),  2.70 

Meat  and  fish,  11.15  Recreation,  3.00 

Milk,  2.79  Avocation,  3.00 

Clothing,  12.00  Literature,  .50 

Heat  and  light,  5.00  Church  and  charity,  .80 

Laundry  and  supplies,  2.00  Remembrances,  .75 

Help,  4.00  Fire  insurance,  .09 

Repairs  and  replenishing,  .50 

Enter  the  above  in  the  expense  account  book. 

How  much  was  left  toward  the  next  month's  expense  ?  Can 
you  improve  on  this?  What  is  the  per  cent  for  food? 
Clothing  ? 

5.  A  girl  14  years  of  age  has  cost  her  parents  an  amount 
equal  to  the  following  items  : 

Food,  $  597. 16  Carfare  to  school,  $  11 .00 

Clothing,  339.66  Doctor,  70.00 

Furniture,  88.65  Dentist,  10.00 

What  is  the  per  cent  for  each  item  ? 

6.  A  family  of  seven  —  three  grown  people  and  four  chil- 
dren —  lived  in  a  southern  city  on  $  600  —  $  50  per  month. 
The  expenses  each  month  were  as  follows  : 

House  rent,  $  12.00  Bread,  $2.50 

Groceries,  12.00  Beef,  2.50 

Washing,  5.00  Vegetables,  2.00 

What  is  the  balance  for  clothing  and  fuel  ?  What  is  the 
per  cent  of  income  spent  for  food  ?  Clothing  ?  Rent  ?  Suggest 
points  of  saving. 


THE    DISTRIBUTION    OF   INCOME  99 

7.  A  girl  in  New  York  City  lives  on  $  10  a  week.  The  ex- 
penses are  as  follows : 

Board  and  washing,  $  300.00  Clothing  and  vacation,  $  95.00 

Luncheons  and  carfare,  100.00  Church  and  charity,  10.00 

How  much  can  she  save  ?  What  is  the  per  cent  for  cloth- 
ing ?  Incidentals  ? 

Can  you  suggest  any  improvements  in  the  distribution  of  her 
income  ? 

8.    A  family  of  four  lives  on  $  750  a  year.     The  expenses 
are  as  follows : 

Rent,  $180.00  Groceries,     including    vegetables, 

Fuel,  52.00  butter,     eggs,    milk,    kerosene, 

Meat,  oysters,  cheese,  95.00  soap,  etc.,  $241.00 

Clothing,  about  145.00 

How  much  is  left  for  the  savings  bank  ?  What  per  cent  for 
rent  ?  Food  ?  Clothing  ?  Operating  expenses  ? 


CHAPTER   V 
FOOD 

SINCE  half  of  the  income  of  the  average  family  is  spent  for 
food,  it  is  important  that  this  expenditure  should  be  made 
intelligently.  Experts  of  the  United  States  Department  of 
Agriculture  estimate  that  the  food  waste  in  a  great  many  of 
the  American  homes  is  as  high  as  20  % .  The  causes  of  waste 
may  be  classified  as  follows :  Needlessly  expensive  material, 
providing  little  nutrition  ;  failure  to  select  according  to  season ; 
great  amounts  thrown  away ;  poor  preparation ;  badly  con- 
structed ovens. 

If  this  waste  were  checked,  it  would  afford  an  increase  in 
the  purchasing  power  of  the  income  which  would  appreciably 
lift  the  family  to  a  higher  plane  of  efficiency.  The  efficiency 
of  every  person  depends  upon  the  energy  and  constant  repair 
of  the  body.  A  woman  should  know  the  cost  of  food  and  real- 
ize what  food  value  she  is  receiving  for  her  money.  It  may 
seem  strange,  but  it  is  true,  that  "a  Roman  feast,  a  Lenten 
fast,  a  Delmonico  dinner,  and  the  lunch  of  the  wayside  beggar 
contain  the  same  few  elements  of  nutrition." 

The  art  of  cooking  can  transform  the  common  but  nutritious  foods 
into  the  most  appetizing  dishes.  Further  than  this,  the  freshness  and 
attractiveness  of  the  food,  the  way  in  which  it  is  served,  the  sur- 
roundings —  all  affect  the  appetite  and  the  power  to  digest.  Cost, 
which  must  always  be  considered  in  the  limited  income  in  relation  to 
the  nutritive  value  of  food,  is  influenced  by  an  equally  important  factor 
—  waste. 

The  problem  of  feeding  our  bodies  is  primarily  a  question  of  supply 
and  demand.  Of  course,  the  element  of  pleasure  in  eating  is  a  properly 

100 


FOOD 


normal  one,  for  enjoyment  aids  digestion.  We  must,  however,  eat  to  live 
rather  than  live  to  eat. 

Every  motion  of  the  body  and  every  thought  in  the  brain  destroy  cer- 
tain tissues.  This  material  must  be  replaced  from  the  food  we  eat.  The 
two  objects  of  eating  are  tissue  repair  in  the  adult  and  tissue  repair 
plus  growth  in  the  child.  As  soon  as  we  realize  that  these  two  pur- 
poses should  determine  the  character  of  the  food  we  eat,  then  we 
shall  know  the  importance  of  intelligent  instead  of  haphazard  choice  of 
food. 

To  repair  the  body  means  to  supply  the  elements  needed  to  renew  the 
tissues  that  are  worn  or  destroyed.  We  can  separate  the  elements  of  the 
human  body  broadly  into  water,  protein,  carbohydrates,  fats,  and  ash. 
Water  composes  60  per  cent  of  a  normal  man's  body.  In  other  words, 
a  200-pound  man  is  composed  of  only  80  pounds  of  solids,  of  which  18 
per  cent  is  composed  of  protein,  15  per  cent  of  fat,  1  per  cent  of  carbo- 
hydrates, and  6  per  cent  of  ash. 

Water  aids  digestion  and  is  necessary  in  the  economy  of  life.  Protein 
is  the  basis  of  bone,  muscle  and  other  tissues,  and  essential  to  the  body 
structure.  Fat  is  an  important  source  of  energy  in  the  form  of  heat 
and  muscular  power.  Carbohydrates  are  transformed  into  fat  and  are 
important  constituents,  though  in  small  proportions  in  the  human  body. 
Ash  is  composed  of  potash,  soda,  and  phosphates  of  lime,  and  is  necessary 
in  forming  bone.  The  diet  best  fitted  to  supply  all  the  needs  of  the  healthy 
human  organism  must  contain  a  correct  proportion  of  these  elements ;  it  is 
called  the  balanced  ration. 


Nutritive  Ingredients  (or  Nutrients)  of  Food 

What  has  thus  far  been  said  about  the  ingredients  of  food  and  the  ways 
in  which  they  are  used  in  the  body  may  be  briefly  summarized  in  the 
following  manner : 


Food  as  purchased 
contains 


Edible  portion  .     .     . 
e.g.  flesh  of  meat,  yolk 
and  white  of  eggs,  wheat, 
flour,  etc. 

Refuse. 

e.g.  bones,  entrails,  shells, 

bran,  etc. 


Water 


Nutrients 


Protein 
Fats 

Carbohydrates 
Mineral     mat- 
ters. 


.;     OCATIONAL  MATHEMATICS  FOR  GIRLS 


Repairs  tissues 

All  serve  as 
fuel  to  yield 
I  energy  in  the 
forms  of  heat 
and  muscular 
power. 


in  digestion,  etc. 


Uses  of  Nutrients  in  the  Body 

Protein Forms  tissue 

e  g.  white  (albumen) 

of  eggs,  curd  (casein) 

of    milk,   lean    meat, 

gluten  of  wheat,  etc. 
Fats Are  stored  in  the  body  as  fat 

e.g.  fat  of  meat,  butter, 

olive  oil,  oils  of  corn 

and  wheat,  etc. 
Carbohydrates  ....     Are  transformed  into  fat . 

e.g.  sugar,  starch,  etc. 
Mineral  matters  (ash)    .     Share  in  forming  bone,  assist 

e.g.  phosphates  of  lime, 

potash,  soda,  etc. 

The  views  thus  presented  lead  to  the  following  definitions  :  (1)  Food 
is  that  which,  taken  into  the  body,  builds  tissue  or  yields  energy. 

(2)  The  most  healthful  food  is  that  which  best  fills  the  needs  of  the  man. 

(3)  The  cheapest  food  is  that  which  furnishes   the    largest    amount  of 
nutriment  at  the  least  cost.     (4)  The  best  food  is  that  which  is  at  the  same 
time  most  healthful  and  cheapest. 

EXAMPLES 

Carbohydrates  are  present  in  large  proportions  in  all  the  cereals,  bread, 
and  potatoes,  and  are  almost  100  %  pure  in  sugar.  There  is  a  widespread 
notion  that  starch,  which  is  a  fat-producing  element,  is  mostly  contained 
in  potatoes,  and  many  people  who  wish  to  reduce  flesh  omit  potatoes 
and  substitute  rice  or  larger  quantities  of  bread  or  cereals.  The  fact  is 
that  the  white  potato  contains  only  15  %  carbohydrates  and  the  sweet 
potato  27  %,  while  rice  has  77  %  and  the  breads  range  from  whole  wheat 
bread  at  49  %  to  soda  crackers  at  73  %  and  the  cereals  from  oats  at  69  % 
to  rye,  78  %. 

1.  How  many  ounces  of  carbohydrates  in  J  Ib.  of  white 
potatoes  ? 

<2.  Find  the  number  of  pounds  of  carbohydrates  in  4  Ib.  of 
rice. 

3.  Find  the  number  of  ounces  of  carbohydrates  in  a  loaf  of 
whole  wheat  bread  (J  Ib.) 


FOOD  103 

4.  How  many  ounces  of  carbohydrates  in  a  2  Ib.  package  of 
Quaker  Oats  ? 

5.  How  many  ounces  of   carbohydrates   in   4   oz.    of   soda 

crackers  ? 

EXAMPLES 

The  proportion  of  ash  in  foods  is  small,  and  as  the  body  requires  6  per 
cent,  we  must  be  sure  to  supply  it  in  the  food.  Salt  cod  has  the  largest 
proportion,  25  per  cent,  and  we  find  it  in  good  quantities  in  butter,  dried 
beef,  smoked  herring,  and  bacon. 

Of  the  proteins,  lean  meat  is  the  one  most  easily  digested  and  assim- 
ilated. Curiously  enough,  dried  beef  has  the  largest  proportion  of  pro- 
tein of  any  flesh  meat,  30  per  cent,  while  next  in  range  are  leg  of  lamb, 
beef  steak,  roast  beef,  and  fowl,  with  about  18  per  cent. 

Let  us  note  the  protein  value  of  fish.  Smoked  herring,  despised  by 
many,  contains  36  per  cent  of  protein,  salt  cod  and  canned  salmon  21  per 
cent,  and  perch,  halibut,  mackerel,  and  fresh  cod  average  18  per  cent, 
equal  in  food  value  per  pound  to  the  best  beef  and  fowl.  The  peanut  has 
27  per  cent  of  its  weight  protein,  and  peanut  butter  29  per  cent. 

Fat  is  found  in  large  proportion  in  nuts,  especially  in  walnuts,  which 
contain  63  per  cent,  and  cocoanuts  57  per  cent.  Bacon  contains  67  per 
cent  of  fat,  and  butter  85  per  cent. 

1.  If  a  man  weighs  189  pounds,  how  many  pounds  of  water 
in  his  weight  ?     How  many  pounds  of  solids  ?     How  many 
pounds  of  fat  ?  protein  ?  carbohydrates  ? 

2.  How  many  ounces  of  protein  in  a  pound  and  a  half  dried 
beef  ? 

3.  Give  the  number  of  ounces  of  protein  in  a  pound  fowl. 

4.  Give  the  number  of  ounces  of  protein  in  1^  Ib.  of  herring. 

5.  How  many  ounces  of  fat  in  li  Ib.  of  shelled  walnuts  ? 

Kitchen  Weights  and  Measures 

Correct  measurements  are  absolutely  necessary  to  insure 
successful  results  in  cooking. 

Sift  flour,  meal,  powdered  sugar  and  soda  before  measuring. 
Many  articles  settle  hard  or  in  lumps  and  should  be  stirred 
and  pulverized  before  measuring. 


104       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

Measure  all  materials  level  full,  leveling  with  knife.  Do 
not  pack  powdered  articles.  Butter,  lard,  etc.,  should  be 
packed  in  measure  and  leveled. 

A  half  spoonful  should  be  taken  lengthwise  and  not  crosswise. 
A  quarter  spoonful  should  be  taken  by  dividing  a  half  crosswise. 
A  third  spoonful  is  obtained  by  dividing  twice  crosswise. 

EQUIVALENTS  To  MAKE  ONE  POUND 

3  teaspoons  equal  1  tablespoon.         4  cups  flour. 

4  tablespoons  equal  \  cup.  2£  cups  corn  meal. 
2  cups  equal  1  pint.  2|  cups  oatmeal. 

2  pints  equal  1  quart.  6  cups  rolled  oats. 

4  quarts  equal  1  gallon.  4^  cups  rye  meal. 

4  cups  flour  equal  1  Ib.  2  cups  rice. 

2  cups  sugar  equal  1  Ib.  2  cups  granulated  sugar. 

16    tablespoons  dry   ingredients      2f  cups  brown  sugar. 

equal  1  cup.  2f  cups  powdered  sugar. 

12  tablespoons  liquid  equal  1  cup.       3J  cups  confectioner's  sugar. 

2  cups  butter. 

2  cups  chopped  meat.    . 

4|  cups  ground  coffee. 

t.  is  the  abbreviation  for  teaspoonful;  and  £&.,  for  tablespoonful. 

EXAMPLES 

1.  How  many  teaspoons  in  4  tablespoons  ? 

2.  How  many  tablespoons  in  j  cup  ? 

3.  How  many  cups  are  equivalent  to  5  pints  ? 

4.  Give  the  number  of  tablespoons  in  a  pint. 

5.  Give  the  number  of  teaspoons  in  3  quarts  and  1  pint. 

6.  A  cup  of  flour  weighs  how  many  ounces  ?     What  part 
of  a  pound  ? 

7.  How  many  cups  will  56  tablespoons  of  baking  soda  fill  ? 

8.  A  pint  of  liquid  contains  how  many  tablespoons  ? 

9.  A  cup  of  sugar  weighs  how  many  ounces  ? 

10.    Two  cups  of  corn  meal  is  what  part  of  a  pound  ? 


FOOD  105 

11.  Give  the  weight  in  ounces  and  fractions  of  a  pound  of 
the  following  quantities  :  — 

(a)  1  cup  of  butter.  (/)  1  ,cup  of  powdered  sugar. 

(b)  1  cup  of  rice.  (g)  1  cup  of  brown  sugar. 

(c)  3  cups  chopped  meat.  (7i)  1  cup  of  rye  meal. 

(d)  1  cup  of  coffee.  (i)   1  cup  of  oatmeal. 

(e)  1  cup  of  conf.  sugar. 

12.  What  is  the  cost  of  each  of  the  following : 

(a)  1  cup  of  oatmeal  at  5  cts.  a  pound  ? 

(b)  2  cups  of  sugar  at  5  Ibs.  for  33  cts.? 

(c)  2i  cups  of  rice  at  5  cts.  a  pound  ? 

(d)  i  cup  of  milk  at  8  cts.  a  quart  ? 

(e)  J  cup  of  butter  at  35  cts.  a  pound  ? 
(/)  2  eggs  at  38  cts.  a  dozen  ? 

(g)  |  peck  of  potatoes  at  72  cts.  a  bushel  ? 

(h)  31  level  teaspoons  of  sugar  at  8  cts.  a  pound  ? 

(i)    i  cup  of  vinegar  at  9  cts.  a  quart. 

Cost  of  Food 

In  order  to  calculate  the  cost  of  food  it  is  necessary  to  know 
price  per  pound,  price  per  cupful,  and  even  price  per  teaspoon- 
ful.  The  price  should  be  calculated  to  three  decimal  places 
and  the  results  tabulated  as  follows  : 

Cost  per  pound  or  quart. 

Number  of  cupfuls  in  pound  or  quart. 

Cost  per  cupful. 

Cost  per  tablespoonful. 

Cost  per  teaspoonful. 

When  it  is  once  calculated  the  data  may  be  used  from  day 
to  day  in  calculating  the  cost  of  food. 

EXAMPLES 

1.  What  is  the  cost  per  teaspoonful  of  cocoa  at  38  cents  a 
pound  ?  (4  cups  in  a  pound.) 


106        VOCATIONAL   MATHEMATICS   FOR   GIRLS 

2.  What  is  the  cost  of  a  third  of  a  cup  of  powdered  sugar 
at  10  cents  a  pound  ?     (2  J  cups  in  a  pound.) 

3.  What  is  the  cost  of  a  tablespoonful  of  cream  at  23  cents 
a  pint  ? 

4.  What  is  the  cost  of  2  teaspoonfuls  of  sugar  at  6-J-  cents 
a  pound  ?     (2  cups  in  a  pound.) 

5.  What  is  the  cost  of  6  nuts  at  20  cents  a  pound  ?     (29 
walnuts  in  a  pound.) 

6.  What  is  the  cost  of  6  tablespoons  of  coffee  at  35  cents  a 
pound  ?     (41  cups  of  coffee  in  a  pound.) 

7.  What  is  the  cost  of  3  slices  of  toast  at  5  cents  a  loaf  ? 
(10  slices  in  a  loaf.) 

8.  What  is  the  cost  of  a  pat  of  butter  at  38  cents  a  pound  ? 
(16  pats  of  butter  in  a  pound.) 

9.  What  is  the  cost  of  an  ordinary  serving  of  cornflakes 
at  10  cents  a  pound  ?     (15  servings  in  a  pound.) 

10.  What  is  the  cost  of  a  serving  of  cream  (f  of  cup)  at 
24  cents  a  pint  ? 

11.  What  is  the  cost  of  an  ordinary  serving  of  macaroni  at 
12  cents  a  pound  ?     (11  servings  to  the  pound.) 

12.  What  is  the  cost  of  a  serving  of  cheese  at  20  cents  a 
pound  ?     (9  servings  in  a  pound.) 

13.  What  is  the  cost  of  a  serving  of  cabbage  salad  if  cab- 
bage is  3  cents  a  pound  and  two  servings  in  a  pound?     (A 
tablespoonful  of  salad  dressing  of  equal  parts  of  oil  and  vinegar 0 
Oil  is  25  cents  a  half  pint.     Vinegar  is  10  cents  a  quart.) 

14.  What  is  the  cost  of  a  serving  of  stewed  apricots  at  18 
cents  a  pound  ?     (A  half  pound  of  sugar  at  7  cents  is  added 
to  the  apricots.     Nine  servings  in  a  pound.) 


FOOD  107 

15.  What  is .  the    cost  of  an   ordinary  serving   of   mashed 
potatoes  at  25  cents  a  half  peck  ?     (A  teaspoonful  of  milk  at 
8  cents  a  quart  to  each  serving.     A  half  pat  of  butter  at  37 
cents  a  pound,  sixteen  pats  in  a  pound.     Twenty-one  servings 
in  a  half  peck.) 

16.  What  is  the  cost  of  a  serving  of  grape  jelly  (1  oz.)  at 
13  cents  a  pound  ? 

Girls  should  know  how  to  make  out  a  tabulation  of  stand- 
ard food  materials,  the  current  price  for  such  material  at  the 
local  stores,  and  the  cost  of  quantities  commonly  used  in  cook- 
ing, as  one  cup  or  one  tablespoonful.  They  should,  in  addi- 
tion, know  how  to  take  common  recipes  that  are  used  in  cook- 
ing classes  'and  reckon  the  cost.  This  will  aid  in  reckoning 
the  cost  of  meals  and  arranging  them  economically.  In  a  like 
manner,  the  cost  of  meals  for  one  day  and  for  one  week  may 
be  calculated  to  see  how  near  they  are  living  within  their 
income. 

EXAMPLES 

1.  A  supper  consisting  of  the  following  is  served  for  14 
people :  codfish  in  tomato  sauce,  cereal  muffins,  cookies,  and 
tea.     What  is  the  cost  per  person  if  the  codfish  costs  30  cents, 
the  muffins  24  cents,  the  cookies  34  cents,  the  tea  10  cents, 
and  fuel  5  cents  ? 

2.  What  is   the  cost  per   person   for   the   following  meal 
when  14  are  served  ?     The  meal  consists  of  milk  toast,  stewed 
prunes  with  lemon,  chocolate  layer  cake,  and  tea.     The  milk 
toast  costs  25  cents,  the  prunes  25  cents,  the  cake  50  cents, 
the  tea  10  cents,  and  fuel  10  cents. 

3.  In  a  pound  of  rolled  oats,  costing  8  cents,  there  are  4 
cups.     What  is  the  cost  of  a  serving  (J  cup)  of  rolled  oats  ? 

4.  In  a  package  of  cream  of  wheat  costing  14  cents  there 
are  41  cups.     One  eighth  of  a  cup  is  necessary  for  a  serving. 
What  is  the  cost  of  a  serving  ? 


108       VOCATIONAL   MATHEMATICS   FOR   GIRLS 


5.    Compute  the  cost  of  a  cup  of  white  sauce  from  the  fol- 
lowing recipe : 


1  cup  milk 
4£  t.  flour 
4£  t.  butter 
t.  salt 


milk,  9c  a  quart 
flour,  5c  a  pound 
butter,  39c  a  pound 
salt  Ic  a  cup 


6.  A  dinner  consisting  of  mashed  potatoes,  peas,  rib  roast, 
rolls,  jelly,  fruit  salad,  krummel  torte,  coffee,  cream  and  sugar 
is  served  for  six.  What  is  the  cost  per  person?  Estimate 
portions  from  amounts  given. 

DISHES  AMOUNTS 

Mashed  potatoes    £  pk.  potatoes  at  45c  per  pk. 

1^  cups  milk  at  2c  per  cup 

3  tablespoons  butter  at  40c  per  Ib. 
Peas  6  tablespoons  or  £  can  at  13c  per  can 

Rib  roast  f  of  4-lb.  roast  at  28c  per  Ib. 

Gravy  3  cups  flour  at  .  l|c  per  cup 

Rolls  ^  cup  milk  at  2c  per  cup 

3  tablespoons  sugar,  2  tablespoons  butter,  f  yeast  cake 

at2c 

Jelly  £  glass  at  lOc  per  glass 

Apple  and  3  apples  at  8c  per  doz. 

grape  salad         \  Ib.  grapes  at  lOc  per  Ib. 
Saratoga  flakes       \  package  at  15c  per  package 
Salad  dressing         \  cup  vinegar  at  8c  per  qt. 

1  egg  at  30c  per  doz. 

3  tablespoons  sugar  at  7c  per  Ib. 

1  tablespoon  butter  at  40c  per  Ib. 
Krummel  Torte     \  package  dates  at  lOc  per  package 

f  cup  nuts  at  70c  per  Ib.,  3  cups  per  Ib. 

\\  eggs  at  30c  per  doz. 

\  pt.  whipping  cream  for  torte  as  well  as  for  coffee  at  15c 

Coffee  6  tablespoons  at  34c  per  Ib. 

Sugar  3  teaspoons 

Sugar  total  7  tablespoons  =  TV  cup  at  7c  per  Ib. 

Butter  total  6  tablespoons  -  f  cup  at  40c  per  Ib. 


FOOD  109 

7.  The   following  breakfast  and  luncheon  were  served  for 
six.     What  was  the  cost  of  each  meal  per  person  ? 

DISHES  AMOUNT  PER  PERSON 

Orange  1  medium-sized,  30c  a  doz. 

Toast  2  thin  slices,  ic  a  slice 

Butter  1  ordinary  pat,  £c 

Egg  1  medium-sized,  3c 

Corn  flakes  1  ordinary  serving,  .2c 

Cream  f  cup,  15c  \  pt. 

Sugar  3|  level  teaspoons,  7c  Ib. 

Coffee  2£  tb.  at  34c  per  Ib 

Luncheon 

Macaroni  Ordinary  serving,  4c 

and  cheese  f  cu.  in.,  .02c 

Cabbage  salad  Large  serving,  .02c 

Cooked  dressing  1  tablespoon,  .OO^c 

Stewed  apricots  1  serving,  2c 

Doughnut  1  large,  Ic 

Milk  1  cup,  3c 

8.  The  following  dinner  was  served  for  six.     What  is  the 
cost  per  person  ? 

DISHES  AMOUNT  PER  PERSON 

Rib  roasfc        1  Fairly  large  serving,  9c 
Brown  gravy  J 

Butter  Ordinary  pat,  £c 

Mashed  potatoes  Ordinary  serving,  £c 

Peas  Very  small,  £c 

Jelly  Very  small,  Ic 

Buns  2  buns,  Ic  apiece 

Apple  and  £  apple,  Jc 

grape  salad  \  oz.  of  grapes,  Ic 

Cooked  dressing  1  tablespoon,  ^c 

Saratoga  flakes  3  portions,  lOc  a  pkg.  (12  portions) 

Krummel  Torte 

Dates  6  dates,  lOc  a  Ib.  (30  dates  in  a  Ib.) 

Nuts  6  nuts,  18c  a  Ib.  (22  nuts  in  a  Ib.) 

Whipping  cream  1  tablespoon,  15c  \  pt. 

Sugar  2  teaspoons,  7c  a  Ib. 

Cream  1  tablespoon,  25c  a  pt. 


110       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

9.  The  recipe  for  potato  soup  for  a  family  of  man,  wife,  and 
two  children  is  : 

3  large  potatoes  2  tb.  flour 

1  qt.  milk  1|  t.  salt 

2  slices  onion  dash  pepper 

3  tb.  butter  1  t.  chopped  parsley 

a.  What  is  the  recipe  for  five  men,  two  women,  and  three 
children  (consider  a  child's  diet  one-half  a  man's  diet,  and  a 
woman's  equal  to  a  man's)?  b.  What  is  the  recipe  for  one 
person  (adult)  ? 

10.  The  recipe  for  a  vegetable  soup  for  a  family  of  husband, 
wife,  and  two  children  is  : 

Beef,  1  Ib.  1^ -  qt.  water 

Bones,  1  Ib.  5  tb.  butter 

£  cup  carrot  1  tb.  finely  chopped  parsley 

\  cup  turnip  salt 

\\  cups  potato  pepper 

\  onion 

a.  What  is  the  recipe  for  a  family  of  three  men,  two 
women,  and  a  child  ?  b.  What  is  the  recipe  for  a  child  ? 

11.  The  recipe  for  sour-milk  biscuits  for  a  family  of  hus- 
band, wife,  and  two  children  is  : 

2£  c.  flour  1  tb.  fat  (lard  or  butter) 

1  t.  salt  1  c.  sour  milk,  or  \  c.  sour  milk 

£  t.  soda  £  c  water 

a.  What  is  the  recipe  for  a  man,  wife,  two  boarders,  and 
five  children  ?  6.  What  is  the  recipe  for  one  adult  ? 

Food  Values 

The  heating  value  of  food  is  measured  by  the  amount  of  heat 
given  off  when  burned.  The  food  taken  into  the  human  system 
is  oxidized  slowly  in  order  to  give  us  the  ability  to  do  work ; 


FOOD  111 

the  number  of  heat  units  that  food  is  capable  of  giving  a  body 
represents  the  quantity  of  energy  the  food  will  provide. 

There  are  two  units  for  measuring  heat :  the  English  and  metric  unit. 
The  English  unit  is  called  a  Calorie,  and  it  represents  the  quantity  of  heat 
necessary  to  raise  a  pound  of  water  four  degrees  on  the  Fahrenheit  scale. 
The  metric  unit  is  also  called  a  calorie  and  is  the  amount  of  heat  neces- 
sary to  raise  a  gram  of  water  one  degree  on  the  Centigrade  scale.  The 
English  unit  is  called  a  large  Calorie  and  is  represented  by  the  large  letter 
C  while  the  metric  unit  is  called  a  small  calorie  and  is  represented  by  the 
small  letter  c. 

All  scientific  experiments  are  conducted  in  the  metric  system,  while 
our  measurements  in  daily  life  are  in  the  English  system.  It  is  only  nec- 
essary to  know  the  English  unit,  which  is  used  in  this  book. 

The  United  States  Department  of  Agriculture 

The  Department  Bulletin  No.  28  gives  the  fuel  value  of  foods.  It  may 
be  well  to  know  how  the  fuel  value  is  determined.  To  illustrate :  What 
is  the  fuel  value  of  flour  ?  Careful  experiments  by  the  Department  of 
Agriculture  show  that  flour  is  composed  of  10.6  %  protein,  1.1  °/o  fat,  and 
76.5  %  carbohydrates.  Other  experiments  have  shown  that : 

1  gram  of  protein  yields  4100  Calories  (C) 
1  gram  of  fat  yields  9300  Calories  (C) 
1  gram  of  carbohydrates  yields  4100  Calories  (C) 
or  1  ounce  of  protein  yields  113  Calories  (C) 

1  ounce  of  fat  yields  255  Calories  (C) 
1  ounce  of  carbohydrates  yields  113  Calories  (C) 
Then  each  ounce  of  flour  contains 
0.106  ounce  protein 
0.011  ounce  fat 
0.763  ounce  carbohydrates 

Since  each  ounce  of  protein  yields  113  C,  0.106oz.  will  yield  113  x  0.106, 
or  11.98  C.  0.011  oz.  of  fat  will  yield  255  x  0.011,  or  2.81  C.  0.763  oz. 
of  carbohydrates  will  yield  0.763  x  113,  or  86.22  C. 

EXAMPLES 

1.  Rice  contains  6  %  protein,  79.5  %  carbohydrates,  and 
0.7  °/0  fat.  What  is  the  fuel  value  of  3  oz.  rice  ? 


112       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

2.  Milk  contains  4  %  protein,  5  %  carbohydrates,  and  4  % 
fat.     What  is  the  fuel  value  of  8  oz.  milk  ? 

3.  Beans  contain  23.1  °/0  protein,  57  %  carbohydrates,  and 
2  %  fat.     What  is  the  fuel  value  of  5  oz.  beans  ? 

4.  Chicken  contains  24.4  %  protein  and  2  %  fat.     What  is 
the  fuel  value  of  7  oz.  chicken  ? 

5.  Pork  (shoulder)  contains  16  %  protein  and  32.8  %  fat. 
What  is  the  fuel  value  of  2  Ib.  pork  ? 

6.  Butter  contains  0.6  °/0  protein,  0.5  %  carbohydrates,  and 
85  %  fat.     Wrhat  is  the  fuel  value  of  1  Ib.  butter  ? 

7.  Eggs  contain  14.9  %  protein  and  10.5  %  fat.     What  is  the 
fuel  value  of  7  oz.  eggs  ? 

8.  Cornmeal  contains  9.2  %  protein,  70.6  %  carbohydrates, 
and  3.8  %  fat.     What  is  the  fuel  value  of  3  Ib.  cornmeal  ? 

9.  English  walnuts    contain   16.6  °/0   protein,  63.4  %   carbo- 
hydrates, and  16.1%   fat.     What  is  the  fuel  value  of  f  Ib. 
nuts  ? 

It  is  clear  that  a  balanced  ration  need  not  be  an  expensive  one.  The 
amount  of  heat  required  by  the  body  varies  from  2000  to  3500  calories 
approximately,  dependent  upon  age,  occupation,  and  sex.  A  family  of  a 
working  man,  wife,  and  three  children  under  sixteen  years  of  age  requires 
12,000  total  calories,  1200  to  1800  of  protein,  or  from  10  to  25%  of  the 
total  amount  required.  The  quantity  of  food  taken  at  each  meal  may 
vary,  provided  the  total  quantities  each  day  reach  the  standard  required. 
Some  authorities  suggest  about  four-twelfths  for  breakfast,  three-twelfths 
for  luncheon,  and  five-twelfths  for  dinner. 

There  are  two  defects  in  American  diet.  First,  we  fail  to  have  a  bal- 
anced ration  and,  second,  we  think  that  the  richer  the  food  the  more 
nourishing  it  is,  and  that  its  goodness  is  in  proportion  to  the  hours  spent 
in  its  preparation. 

The  protein  is  the  most  valuable  and  expensive  part  of  the  food  supply 
and  it  is  wise  to  have  a  list  of  proteins  so  that  one  can  substitute  the  lesser 
for  the  more  expensive.  Protein,  of  which  we  need  18  %,  is  found  more 
generally  in  fish  than  in  meat,  and  the  inexpensive  peanut  is  an  appe- 
tizing substitute;  fat,  of  which  we  need  15%,  can  be  had  from  the 


FOOD  113 

fat  of  all  meats,  and  carbohydrates  are  better  obtained  from  potatoes 
than  from  rich  cakes,  confectionery,  and  jellies.  We  are  indebted  to 
modern  inventions  for  a  wide  list  of  cooked  and  partially  cooked  foods 
which  have  economized  the  time  of  the  busy  housewife  and  which  have 
enriched  our  breakfast  table  beyond  that  of  other  nations.  The  breakfast 
cereals  and  the  grains  from  which  they  are  made,  white  bread,  potatoes, 
sugar,  butter,  and  other  fats  may  be  classed  as  carbohydrates,  while  meat, 
fish,  eggs,  milk,  cheese,  peas,  beans,  and  cabbage  are  some  of  the  repre- 
sentatives of  the  protein  group.  These  carbohydrates  and  nitrogenous 
substances  are  not  wholly  such,  but  are  more  or  less  a  mixture  of  other 
things. 

Making  Up  Menus 

In  making  up  menus  it  is  necessary  to  have  them  balance 
evenly.  One  should  not  have  too  much  fat  one  day,  too  much 
starch  the  next,  etc.  The  menus  for  each  day  should  hold 
part  of  each  kind  of  food,  one  meat  (fish  or  eggs),  one  fat,  one 
starch,  one  tonic  vegetable,  and  one  laxative  vegetable  or 
fruit. 

The  summer  menus  must  be  compiled  most  carefully,  for 
too  much  fat  or  too  much  meat  tends  to  heat  the  body  at  an 
excessive  rate  and  should  therefore  be  avoided. 

Of  the  different  food  materials  which  are  palatable,  nutritious,  and 
otherwise  suited  for  nourishment,  we  should  select  those  that  furnish  the 
largest  amounts  of  available  nutrients  at  the  lowest  cost.  To  do  this  it 
is  necessary  to  take  into  account  not  only  the  price  per  pound,  quart,  or 
bushel  of  the  different  materials,  but  also  the  kinds  and  amounts  of  the 
actual  nutrients  they  contain  and  their  fitness  to  meet  the  demands  of 
the  body  for  nourishment.  The  cheapest  food  is  that  which  supplies  the 
most  nutriment  for  the  least  money.  The  most  economical  food  is  that 
which  is  cheapest  and  at  the  same  time  best  adapted  to  the  needs  of  the 
user. 

There  are  various  ways  of  comparing  food  materials  with  respect  to  the 
relative  cheapness  or  expensiveness  of  their  nutritive  ingredients.  The  best 
way  of  estimating  the  relative  pecuniary  economy  of  different  food  mate- 
rials is  found  in  a  comparison  of  the  quantities  of  nutrients  and  energy 
which  can  be  obtained  for  a  given  sum,  say  10  cents,  at  current  prices. 
This  is  illustrated  in  the  table  which  follows  : 


114       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


COMPARATIVE  COST  or  DIGESTIBLE  NUTRIENTS  AND  ENERGY  IN 

DIFFERENT  FOOD  MATERIALS  AT  AVERAGE  PRICES 
[It  is  estimated  that  a  man  at  light  to  moderate  muscular  work  requires 
about  0.23  pounds  of  protein  and  3050  Calories  of  energy  per  day.] 


KIND  OF  FOOD  MATERIAL 

« 

i_! 

M 
H 
P* 

1 

3 
p* 

COST  OP  1  LB.  PRO- 
TEIN l 

ICosT  OF  1,000  CAL- 
ORIES ENERGY  (a) 

AMOUNT  FOR  10  CENTS 

Total  weight  of 
food  material 

Protein 

1 

Carbohydrates 

>, 

SP 

CD 

C 

W 

Beef,  sirloin      .... 
Do    .... 

Cents 
25 
20 
15 
16 
14 
12 
12 
9 
5 
25 
16 
20 
16 
12 
22 
18 
12 
10 
18 
7 
10 
12 

25 
18 

Dollars 
1.60 
1.28 
.96 
.87 
.76 
.65 
.75 
.57 
.35 
.98 
1.22 
1.37 
1.10 
.92 
1.60 
1.30 
6.67 
.93 
1.22 
.45 
.74 
.57 

4.30 
3.10 

Cents 
25 
20 
15 
18 
16 
13 
17 
13 
7 
32 
11 
22 
18 
10 
13 
11 
3 
46 
38 
22 
9 
13 

111 
80 

Lbs. 
0.40 
.50 
.67 
.63 
.71 
.83 
.83 
1.11 
2 
.40 
.63 
.50 
.63 
.83 
.45 
.56 
.83 
1 
.56 
1.43 
1 
.83 

.40 
.56 

Lbs. 
0.06 
.08 
.10 
.11 
.13 
.15 
.13 
.18 
.29 
.10 
.08 
.07 
.09 
.11 
.06 
.08 
.02 
.11 
.08 
.22 
.13 
.18 

.02 
.03 

Lbs. 
0.06 
.08 
.11 
.08 
.09 
.10 
.08 
.10 
.23 
.03 
.17 
.07 
.09 
.19 
.14 
.18 
.68 

.02 
.01 
.20 
.10 

.01 

Lbs. 

.01 
.02 

Calories 
410 
515 
685 
560 
630 
740 
595 
795 
1,530 
315 
890 
445 
560 
1,035 
735 
915 
2,950 
220 
265 
465 
1,135 
760 

90 
125 

Do    .... 

Beef,  round      .... 
Do          .     . 

Do    .     . 

Beef,  shoulder  clod    . 
Do    . 

Beef,  stew  meat    .     .     . 
Beef,  dried,  chipped  .     . 
Mutton  chops,  loin    . 
Mutton,  leg      .... 
Do 

Roast  pork,  loin    .     . 
Pork,  smoked  ham    . 
Do    

Pork,  fat  salt    .... 
Codfish,  dressed,  fresh  . 
Halibut,  fresh  .... 
Cod,  salt       
Mackerel,  salt,  dressed  . 
Salmon,  canned    .     .     . 
Oysters,  solids,  50  cents 
per  quart  
Oysters,  solids,  35  cents 
per  quart  . 

1  The  cost  of  1  pound  of  protein  means  the  cost  of  enough  of  the  given  ma- 
terial to  furnish  1  pound  of  protein,  without  regard  to  the  amounts  of  the  other 
nutrients  present.  Likewise  the  cost  of  energy  means  the  cost  of  enough  ma- 
terial to  furnish  1000  Calories,  without  reference  to  the  kinds  and  proportions 
of  nutrients  in  which  the  energy  is  supplied.  These  estimates  of  the  cost  of 
protein  and  energy  are  thus  incorrect  in  that  neither  gives  credit  for  the  value 
of  the  other. 


FOOD 


115 


COMPARATIVE  COST  OF  DIGESTIBLE  NUTRIENTS  AND  ENERGY  IN 
DIFFERENT  FOOD  MATERIALS  AT  AVERAGE  PRICES  —  (Continued} 


KIND  OF  FOOD  MATERIAL 

ed 

t-1 

a 

W 

PH 

1 

£ 

1 

3* 

:• 

o 

1 

u 

AMOUNT  FOB  10  CENTS 

^  >. 

§g 

;! 

o 

H  W 

Ji 

2*3 
|| 
11 

31 

£* 

e 

1 

PH 

1 

1 

T3 
>, 

1 

£ 

a/ 
C 
W 

Lobster,  canned  .  .  . 
Butter  .  . 

Cents 
18 
20 
25 
30 
24 
16 
8 
16 

!J 

3 

'4 
2^ 

F> 

8 
6 
5 
4 
5 
5 

2| 

5 
10 

I1 

1 

I* 

6 

7 
6 

Dollars 
1.02 
20.00 
25.00 
30.00 
2.09 
1.39 
.70 
.64 
1.09 
.94 
.31 
.26 
.32 
.73 
.53 
.29 
1.18 
.77 
.64 
.51 
.65 
.29 
2.08 
6.65 
4.21 
1.00 
.67 
.60 
1.33 
5.00 
10.00 
12.00 
8.75 

Cents 
46 
6 
7 
9 
39 
26 
13 
8 
11 
10 
2 
2 
2 
4 
4 
2 
5 
5 
4 
3 
4 
3 
22 
77 
23 
5 
3 
3 
8 
8 
27 
40 
47 
3 

Lbs. 
.56 
.50 
.40 
.33 
.42 
.63 
1.25 
.63 
2.85 
3.33 
3.33 
4 
4 
1.33 
1.33 
2.50 
1.25 
1.67 
2 
2.50 
2 
2 
4 
2 
1 
6.67 
10 
13.33 
10 
6.67 
1.43 
1.67 
1.43 
1.67 

Lbs. 
.10 
.01 

.05 
.07 
.14 
.16 
.09 
.11 
.32 
.39 
.31 
.13 
.19 
.34 
.08 
.13 
.16 
.20 
.15 
.35 
.05 
.02 
.02 
.1 
.15 
.20 
.08 
.02 
.01 
.01 
.01 

Lbs. 
.01 
.40 
.32 
.27 
.04 
.06 
.11 
.20 
.11 
.13 
.03 
.04 
.07 
.02 
.09 
.16 

.02 
.02 
.03 
.01 
.03 
.01 

.01 
.01 
.01 
.01 
.01 
.02 
.01 

.01 

Lbs. 

.02 
.14 
.17 
2.45 
2.94 
2.96 
.98 
.86 
1.66 
.97 
.87 
1.04 
1.30 
1.04 
1.16 
.18 
.05 
.18 
.93 
1.40 
1.87 
.54 
.65 
.18 
.13 
.09 
1.67 

Calories 
225 
1,705 
1,365 
1,125 
260 
385 
770 
1,185 
885 
1,030 
5,440 
6,540 
6,540 
2,235 
2,395 
4,500 
2,025 
2,000 
2,400 
3,000 
2,340 
3,040 
460 
130 
430 
1,970 
2,950 
3,935 
1,200 
1,270 
370 
250 
215 
2,920 

Do    

Do    

Eggs,  36  cents  per  doz.  . 
Eggs,  24  cents  per  doz.  . 
Eggs,  12  cents  per  doz.  . 
Cheese  

Milk,  7  cents  per  quart  . 
Milk,  6  cents  per  quart  . 
Wheat  flour      .... 
Do    

Corn  meal,  granular  .     . 
Wheat  breakfast  food    . 
Oat  breakfast  food    . 
Oatmeal  

Rice  .  .  . 

Wheat  bread    .... 
Do    . 

Do    

Rye  bread  
Beans,  white,  dried  .  . 
Cabbage  . 

Celery  .  .  . 

Corn,  canned  .... 
Potatoes,  90  cents  per  bu. 
Potatoes,  60  cents  per  bu. 
Potatoes,  45  cents  per  bu. 
Turnips  

Apples  

Bananas  . 

Oranges  

Strawberries  .... 
Su°"ar  ... 

116       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

EXAMPLES 

1.  What  is  the  most  economical  part  of  beef  for  a  soup  ? 

2.  What  is  the  most  economical  part  of  mutton  for  boiling  ? 

3.  What  is  the  most  economical  part  of  pork  for  a  roast  ? 

4.  Is  fresh  or  salt  codfish  more  economical  ? 

5.  What  is  the  fuel  value  of  3  oz.  oatmeal  ? 

6.  What  is  the  fuel  value  of  3  oz.  rice  ? 

7.  What  is  the  fuel  value  of  4  oz.  strawberries  ? 

8.  What  is  the  fuel  value  of  6  oz.  milk  ? 

EXAMPLES 

Since  several  hundred  Calories  are  required  each  day  for  a  person's 
diet,  it  is  most  convenient  in  computing  meals  to  think  of  our  foods  in 
100-Calorie  portions.  Therefore  it  is  desirable  to  know  how  to  compute 
this  portion  and  tabulate  it  for  future  reference. 

1.  42  qt.  of  milk  give  36,841  Calories.      What  is  the  weight 
of  a  100-C  portion  ? 

2.  3J  Ib.  of  flour  give  1610.5  Calories.     What  is  the  weight 
of  a  100-C  portion  ? 

3.  i  Ib.  of  dates  give  393.75  Calories.     What  is  the  weight 
of  a  100-C  portion  ? 

4.  If  J  of  a  cup  of  flaked  breakfast  food  gives  approximately 
100  C,  what  is  the  food  value  of  1  Ib.? 

5.  If  ^  of  a  cup  of  skimmed  milk  gives  approximately  100 
C,  what  is  the  food  value  of  1  qt.? 

6.  A   teaspoonful  of   fat  gives  100  C.      What  is  the  food 
value  of  1  Ib.  lard  ? 

7.  If  J-  of  a  medium-sized  egg  gives  a  food  value  of  100  C, 
what  is  the  food  value  of  an  egg  ? 

8.  4  thin  slices  of  bacon  (1  oz.)  give  a  food  value  of  100  C. 
What  is  the  food  value  of  9  Ib.  of  bacon  ? 


FOOD 


117 


9.   If  f  oz.  of  sweet  chocolate  has  a  food  value  of  100  C, 
what  is  the  food  value  of  \  lb.? 

10.  Ten  large  pears  have  the  value  of  100  C,  which  is  the 
same  as  for  2  doz.  raisins.     What  is  the  food  value  of  a  single 
raisin  ? 

11.  Find  the  individual  cost  of  feeding  the  following  families 
per  week  and  per  day.     Find  the  number  of  Calories  per  indi- 
vidual per  day.     (Arrange  results  in  a  column  as  suggested.) 

FAMILY        No.  IN  FAMILY        TOTAL  COST        TOTAL  CALORIES 

A  5 

B  7 

C  3 

D  3 

E  7 

F  6 

G  7 

H  4 

I  4 

J  6 

K  8 

L  6 

M  7 

N  14 

O  6 


13.60 

86224 

15.06 

99928.64 

11.21 

101966.75 

6.68 

33744.14 

15.01 

130557.04 

12.89 

93456.34 

17.77 

11063.91 

11.86 

90891.3 

10.23 

50490 

16.47 

69385.9 

10.37 

112197.3 

16.08 

930262 

30.89 

86006.8 

32.91 

141517 

12.31 

85582.8 

Economical  Use  of  Meat 

It  is  important  to  reduce  waste  by  using  as  much  as  possible 
of  the  bone,  fat,  and  trimmings,  not  usually  served  with  the 
meat.  If  nothing  better  can  be  done  with  them,  the  bones  and 
trimmings  are  profitably  used  in  the  soup  kettle,  and  the  fat 
can  be  saved  for  cooking  to  be  used  in  place  of  more  expensive 
butter  and  lard.  The  bits  of  meat  not  served  with  the  main 
dish,  or  remaining  after  the  first  serving,  may  be  seasoned  and 
recooked  in  many  palatable  ways.  Or  they  can  be  combined 
with  vegetables,  pie  crust,  or  other  materials,  thus  extending 
the  meat  flavor  over  a  large  quantity  of  less  expensive  food. 


118       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

Different  kinds  and  cuts  vary  considerably  in  price.  Sometimes  the 
cheaper  cuts  contain  a  larger  proportion  of  refuse  than  the  more  expen- 
sive, and  the  apparent  cost  is  really  more  than  the  actual  cost  of  the 
more  edible  portion.  Aside  from  this  advantage,  that  of  the  more  ex- 
pensive cuts  lies  in  the  tenderness  and  flavor,  rather  than  in  the  nutritive 
value.  Tenderness  depends  on  the  character  of  the  muscle  fibers  arid 
connective  tissues  of  which  the  meat  is  composed.  Flavor  depends 
partly  on  the  fat  present  in  the  tissues,  but  mainly  on  nitrogenous  bodies 
known  as  extractives,  which  are  usually  more  abundant  or  of  more 
agreeable  flavor  in  the  more  tender  parts  of  the  animal.  The  heat  of 
cooking  dissolves  the  connective  tissues  of  tough  meat  and  in  a  measure 
makes  it  more  tender,  but  heat  above  the  boiling  point  or  even  a  little 
lower  tends  to  change  the  texture  of  muscle  fibers.  Hence  tough  meats 
must  be  carefully  cooked  at  low  heat  long  applied  in  order  to  soften  the 
connective  tissue.  For  this  purpose  the  fireless  cooker  may  be  used  to 
great  advantage. 

Steers  and  Beef 

Steers  are  bought  from  the  farmer  by  the  hundredweight 
(cwt.).  They  are  inspected  and  then  weighed.  After  they 
are  killed  and  dressed,  they  are  washed  several  times  and  sent 
to  the  cooler.  The  carcass  must  be  left  in  the  cooler  several 
days  before  it  can  be  cut.  It  is  then  divided  into  eight 
standard  cuts  and  each  piece  weighed  separately. 

Sixty  per  cent  of  the  meat  used  in  this  country  is  produced 
in  the  Federally  inspected  slaughtering  and  packing  houses,  of 
which  there  are  nearly  900,  located  in  240  cities. 

EXAMPLES 

1.  A  steer  weighing  1093  Ib.  was  purchased  for  $  7.42  per 
cwt.     What  was  paid  for  him  ? 

2.  The  live  weight  of  a  steer  is  1099  Ib. ;  the  dressed  weight 
641  Ib.     What  is  the  difference  ?     What  is  the  percentage  of 
beef  in  the  animal  ? 

3.  A  steer  with  a  dressed  weight  of  677  Ib.  was  cut  into  the 
following  parts  :  two  ribs  weighing  61  Ib.  each,  2  loins  103  Ib., 
2  rounds  154  Ib.,  and  suet  21  Ib.     What  was  the  percentage  of 
each  part  to  the  total  amount  ? 


FOOD  119 

4.  A  steer  with  a  dressed  weight  of  644  Ib.  was  sold  at 
$  10.51  per  cwt.     What  was  paid  ? 

5.  If   the  value   of   ribs  is  18^,  loins  18 j£  rounds  9f£ 
what  is  the  value  of  cuts  in  problem  3  ? 

6.  A  housewife  buys  8J  Ib.  of  meat  every  Monday,  9^  Ib. 
on  Wednesday,  and  10J  Ib.  on  Saturday.     What  is  the  total 
amount  of  meat  purchased  in  a  week  ? 

7.  The  live  weight  of  a  low-grade  steer  was  947  Ib.  and 
dressed  weight  475  Ib.     What  is  the  per  cent  of  dressed  to 
live  weight  ?     What   did   the   steer   sell   for  at  6^  cts.  live 
weight  ?     What  was  the  selling  price  per  cwt.  ? 

8.  A  high-grade  steer  weighed  live  weight   1314   Ib.  and 
dressed  weight  897  Ib.     What  is  the  per  cent  of  "dressed  to 
live  weight?     What  did  the  steer  sell  for  at  9  cts.  a  pound 
live  weight  ?     What  was  the  selling  price  per  cwt.  ?     Note 
the  difference  in  the  price  between  low-  and  high-grade  steers 
due  to  the  fact  that  the  latter  have  a  greater  proportion  of  the 
higher  priced  cuts. 

9.  A    steer    was    killed    weighing    632    Ib.    and    sold    for 
$  10.38  cwt.     a.   What  was  the  selling  price  ?     b.   What  was 
the  average  price  per  pound  ?     c.    What  was  the  percentage 
of  each  cut  to  total  value  ?     d.   What  was  the  total  value  of 
each  cut  ? 

CUTS  WEIGHT           PRICE  PER  POUND  (Wholesale) 

2  Ribs  58  Ib.  $  .17 

2  Loins  100  .18£ 

2  Rounds  150  .09f 

2  Chucks  160  .08 

2  Flanks  30  .05| 

2  Shanks  26  .05 

2  Briskets  32  .08£ 

Navel  End  46  .05 

Neck  Piece  8  .Olf 

2  Kidneys  2  .05 

Suet  20  .08 
632  Ib. 


120       VOCATIONAL   MATHEMATICS   FOR   GIRLS 


Cuts  of  Beef 

The  cuts  of  beef  differ  with  the  locality  and  the  packing 
house.  The  general  method  of  cutting  up  a  side  of  beef  is 
illustrated  in  the  following  figure. 


STANDARD  BEEF  CUTS  —  CHICAGO  STYLE 


1  —  Round 

Rump  Roast 
Round  Steak 
Corned  Beef 
Hamburger  Steak 
Dried  Beef 
Shank  —  Soup  Bone 

2  —  Loin 

Sirloin  Steak 
Porterhouse  Steak 
Club  Steak 
Beef  Tenderloin 

3—  Flank 

Flank  Steak 
Hamburger  Steak 
Corned  Beef 


4  —  Ribs 

Rib  Roasts 

5  — Navel  End 

Short  Ribs 
Corned  Beef 
Soup  Meat 

6  —  Brisket 

Corned  Beef 
Soup  Meat 
Pot  Roast 


7  — Fore  Shank 

Soup  Bone 

8  —  Chuck 

Shoulder  Steak 
Shoulder  Roast 
Pot  Roast 

Stews 


FOOD 


121 


STANDARD  PORK  CUTS  — CHICAGO  STYLE 


1  —  Short-cut  Ham 
Ham 

2 — Picnic  Ham 

or  California  Ham 

3  — Boston  Butt 

Pickled  Pork 
Pork  Shoulder 
Pork  Steak 

4  —  Clear  Plate 

Dry  Salt  or  Barrel  Pork 

5  —  Belly 

Bacon 
Spare  Ribs 
Brisket  Bacon 
Salt  Pork 

6—  Loin 

Pork  Roast 
Pork  Chops 
Pork  Tenderloin 

I  —  Fat  Back 

Paprika  Bacon 
Dry  Salt  Fat  Backs 
Barrel  Pork 


EXAMPLES 

Hogs  are  usually  killed  when  nine  or  ten  months  old.  The  weight 
is  75  %  to  80  %  of  live  weight.  The  method  of  cutting  up  a  side  of  pork 
differs  considerably  from  that  employed  with  other  meats.  A  large  por- 
tion of  the  carcass  of  a  dressed  pig  consists  of  almost  clear  fat.  This  fur- 
nishes the  cuts  which  are  used  for  salt  pork  and  bacon. 

1.  A  hog  weighed  at  the  end  of  9  months  249  Ib.     When  he 
was  killed  and  dressed,  he  weighed  203  Ib.     What  was  the 
per  cent  of  dressed  to  live  weight  ? 

2.  A  hog  weighing  251  Ib.  was  sold  for  81  cents  live  weight. 
When  he  was  dressed,  he  weighed  204  Ib.     What  should  he 
sell  for   per   cwt.   (dressed)   in   order  to  cover   the   price  of 
purchase  ? 


122       VOCATIONAL  MATHEMATICS   FOR   G'IRLS 


3.  Sugar-cured  hams  and  bacons  are  made  by  rubbing  salt 
into  the  pieces  and  placing  a  brine  solution  of  the  following 
proportions   over   them   in  a   barrel,   before   smoking   them: 
8  Ib.  salt,  21  Ib.  brown  sugar,  2  oz.  saltpeter  in  four  gallons  of 
water  for  every  100  Ib.  of  meat.    What  percentage  of  the  solu- 
tion is  salt  ?     Sugar  ?     (Consider  a  pint  of  water  equal  to  a 
pound.) 

4.  Sausages  are  made  by  mixing  pork  trimmings  from  the 
ham  with  fat  and  spices,  and  placing  in  casings.     If  3  Ib.  of 
ham  are  added  to  1  Ib.  fat  pork,  what  is  the  percentage  of  lean 
pork? 

STANDARD  MUTTON  CUTS  — CHICAGO  STYLE 
I —Leg 

Leg  of  Mutton 
Mutton  Chops 

2  —  Loin 

Loiu  Roast 
Mutton  Chops 

3  — Hotel  Mack 

Rib  Chops 
Crown  Roast 


4  —  Breast 

Mutton  Stew 

'  5— Chuck 

Shoulder  Roast 
Stew 
Shoulder  Chops 

EXAMPLES 

1.  A  butcher  buys  169  sheep  at  $5.75  a  head.  He  sells 
them  so  as  to  receive  on  the  average  $  6.12i  for  each.  What 
does  he  gain  ? 


FOOD  123 

2.  A   market   man  bought  19   dressed    sheep   for   $81.75. 
What  was  the  average  price  ? 

3.  A  sheep  weighed  138  Ib.  live  weight  and  72  Ib.  dressed. 
What  was  the  per  cent  of  dressed  to  live  weight  ? 

4.  A  dressed  sheep  when  cut  weighed  as  follows  : 

Leg      23.1  Ib,  each  Neck  3.4  Ib.  Breast    8.2  Ib. 

Loin    18.4  Ib.  each  Shoulder    5.1  Ib.  each  Shank    5.3  Ib.  each 

Ribs     15.3  Ib.  each 

What  was  the  total  dressed  weight  ?    What  was  the  percent- 
age of  each  cut  to  the  dressed  weight  ? 

Length  of  Time  Required  to  Cook  Mutton 

Boiling 
Mutton,  per  pound 15  minutes 

Baking 

Mutton,  leg,  rare,  per  pound  ...  10  minutes 

Mutton,  leg,  well  done,  per  pound  .  15  minutes 

Mutton,  loin,  rare,  per  pound      .     .  8  minutes 

Mutton,  shoulder,  stuffed,  per  pound  15  minutes 

Mutton,  saddle,  rare,  per  pound  .     .  9  minutes 

Lamb,  well  done,  per  pound   ...  15  minutes 

Broiling 

Mutton  chops,  French 8  minutes 

Mutton  chops,  English 10  minutes 

EXAMPLES 
Give  the  fraction  of  an  hour  required 

(a)  To  boil  mutton  (2  Ib.). 

(b)  To  bake  leg  of  mutton  (3  Ib.). 

(c)  To  bake  loin  of  mutton  (4  Ib.). 

(d)  To  broil  mutton  chops  (French). 

(e)  To  broil  mutton  chops  (English). 
(/)  To  bake  shoulder  of  mutton  (5  Ib.). 


124       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

Fish  is  a  very  economical  kind  of  food.     It  can  be  obtained 
fresh  at  a  reasonable  figure  in  seacoast  towns. 

1.  During  the  year  1913, 170,000,000  Ib.  of  fish  were  brought 
into  Boston,  and  sold  for  $  7,000,000.     What  was  the  average 
price  per  pound  ? 

2.  If  528,000,000  Ib.  of  fish  were  caught  in  the  waters  of 
New  England  during  the  year  1913,  it  would  represent  one- 
quarter  of  the  catch  of  the  entire  country.     What  is  the  catch 
of  the  entire  country  ? 

3.  A  pound  of  smoked  ham  at  24  cents  contains  16  %  protein, 
while  a  pound  of  haddock  at  7  cents  contains  18  %  protein. 
How  much  more  protein  in  a  pound  of  haddock  than  in  a  pound 
of  ham  ?     (In  ounces.) 

4.  For  the  same  value,  how  much  more  protein  can  you  pur- 
chase in  the  haddock  than  in  the  ham  ? 

5.  A  pound  of  pork  chops  at  25  cents  contains  17  %  protein  ; 
a  pound  of  herring  at  8  cents  contains  19  %.     How  much  more 
protein  is  there  in  the  pound  of  herring  than  in  the  pork  chops  ? 

6.  For  the  same  value,  how  much  more  protein  can  be  pur- 
chased in  the  pound  of  herring  than  in  pork  chops  ? 

7.  A  pound  of  sirloin  steak  at  30  cents  gives  the  same  amount 
of  protein  as  the  pork  chops  in  example  6.    For  the  same  value 
how  much  more  protein  can  be  obtained  from  haddock  than 
from  the  steak  ?     What  per  cent  of  protein  per  pound  in  had- 
dock ?     Use  data  in  Example  3. 

8.  If  fish  can  be  purchased  at  any  time  at  not  over  12  cents 
per  pound,  and  meats  at  not  less  than  20  cents  per  pound,  what 
is  the  per  cent  of  saving  by  buying  fish  ? 

9.  If  5.3  %  of  the  total  expenses  for  foodstuffs  is  for  fish, 
and  22  %  of  the  family  earnings  goes  for  food,  what  is  the 
amount  spent  for  each  ?     Family  income  $  894. 


FOOD  125 

Economical  Marketing 

The  most  economical  way  to  purchase  food  is  to  buy  in  bulk.  Fancy 
packages  with  elaborate  labels  must  be  paid  for  by  the  consumer.  All 
realize  the  convenience  of  package  goods,  the  saving  in  cost  of  preparation 
and  cooking  and  the  ease  with  which  they  are  kept  clean  and  wholesome, 
but  the  additional  expense  is  enormous,  in  sonre  instances  as  high  as  300  °/o . 

EXAMPLES 

1.  If  the  retail  price  of  dried  beef   is  50  cents  a  pound, 
how  much  more  per  pound  do  I  pay  for  dried  beef,  when  I 
purchase  a  package   weighing   3|-   oz.    for   18   cents  ?     What 
per  cent  more  do  I  pay  ? 

2.  Wheat  costs  the  farmer  or  producer  11  cents  per  pound. 
I  purchase  a  package  of  wheat  preparation  weighing  5  oz.  for 
10  cents.     How  much  more  do  I  pay  for  wheat  per  pound  than 
it  costs  to  produce  it  ?     What  per  cent  more  do  I  pay  ? 

3.  Good  apples  cost  $  2.75  per  barrel.     If  I  purchase  a  peck 
for  50  cents,  at  what  rate  am  I  paying  for  apples  per  barrel  ? 
(A  standard  apple  barrel  contains  2-J-  bushels.)     How   much 
would  I  save  a  peck,  if  a  few  families  in  the  neighborhood 
joined  me  in  purchasing  a  barrel  ? 

4.  Codfish  retails  at  17  cents  a  pound.     A  group  of  families 
sent  one  of  their  members  to  the  wharf  and  she  purchased  for 
60  cents  a  codfish  weighing  6  Ib.     How  much  was  saved  per 
pound  ?     What  per  cent  ? 

5.  Print  butter  is  molded  by  placing   a   quantity    of   tub 
butter  in  a  mold.     If  the  tub  butter  costs  34  cts.  a  pound  and 
the  print  butter  42  cts.  a  pound,  how  much  cheaper  (per  cent) 
is  the  tub  butter  than  print  butter?     Does  it  afford  the  same 
nourishment? 

6.  A  pint  can  of  evaporated  milk  costs  10  cents  and  con- 
tains the  food  element  of  2  J  quarts  of  fresh   milk  at   8  cents  a 
quart.     What  is  the  saving  per  quart  of  milk  ? 


126       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

Every  housewife  should  possess  the  following  articles  in  the 
kitchen  so  as  to  be  able  to  verify  everything  she  buys : 

1  good  20-lb.  scale  1  dry  quart  measure 

1  peck  measure  1  liquid  quart  measure 

1  half-peck  measure  00-inch  steel  tape 

1  quarter  peck  measure  -  8-oz.  graduate 

The  above  should  be  tested  and  "  sealed "  by  the  Super- 
intendent of  Weights  and  Measures.  Check  the  goods  bought 
and  see  if  weight  and  volume  agree  with  what  was  ordered. 

EXAMPLES 

1.  If  a  gallon  contains  231  cu.  in.,  how  many  cubic  inches 
are  there  in  a  quart  ? 

2.  If  a  bushel  contains  2150.42  cu.  in.,  how   many   cubic 
inches  are  there  in  a  dry  quart  ? 

3.  If  a  half-bushel  basket  or  box,  heaping  measure,  must 
contain  five-eighths  bushel,  stricken l  measure,  how  many  cubic 
inches  does  the  basket  contain  ? 

4.  A  box  12  by  14  by  16  inches  when   stricken   full  will 
hold  a  heaping  bushel.     How  many  cubic  inches  in  the  box  ? 

5.  A  dealer  often  sells  dry  commodities  by  liquid  measure. 
If  a  quart  of  string  beans  were  sold  by  liquid  measure  for  15 
cts.,  how  much  would  the  customer  lose  ?     What  is  the  differ- 
ence in  per  cent  between  liquid  and  dry  quart  measure  ? 

6.  A  grocer  sold  a  peck  of  apples  to  a  housewife.     As  he 
was  about  to  place  the  apples  in  the  basket,  the  woman  called 
his  attention  to  the  fact  that  the  measure  was  not  "  heaping." 
He   placed   four   more   apples    in   the    measure.     When    she 
reached  home  she  counted  24  apples.     What  would  have  been 
the  per  cent  loss  if  she  had  not  called  his  attention   to  the 
measure  ? 

1  Stricken  measure  is  measure  that  is  not  heaped,  but  even  full. 


FOOD  127 

7.  A  "  five-pound  "  pail  of  lard  was  found  to  weigh  4  Ib. 
11  oz.     What  per  cent  was  lost  to  the  customer  ? 

8.  A  package  (supposed  to  be  a  pound)  sold  for  12  cents 
and   was    found  to  weigh  141  ounces.     How  much  did    the 
consumer  lose  ? 

9.  A  quart  of  ice  cream  was  bought  for  40  cents.     The  box 
was  found  to  be  121  cjc  short.     How  much  did  the  consumer 
lose? 

10.  A  girl  bought  a  quart  of  berries  for  ten  cents.  '•  The  box 
was  found  to  contain  54.5  cu.  in.     How  much  was  lost  ? 

11.  A  pound  of  print  butter  cost  39  cents  and  was  found  to 
weigh  14 J  ounces.     How  much  did  the  consumer  lose  ? 


CHAPTER   VI 
PROBLEMS  ON  THE   CONSTRUCTION  OF  A  HOUSE 

MOST  people  live  either  in  a  flat  or  a  house.  Each  has  its 
advantages  and  its  disadvantages.  The  work  of  a  flat  is  all  on 
one  floor ;  there  are  no  stairs,  halls,  cellars,  furnaces,  and  side- 
walks to  care  for,  and  when  the  building  is  heated  by  steam, 
there  is  only  the  kitchen  fire  or  a  gas  range  to  look  after. 
These  are  the  advantages  and  they  reduce  the  work  of  the 
home  to  very  simple  proportions. 

Then,  too,  it  is  possible  to  find  comfortable  flats  at  a  moderate  price  in  a 
neighborhood  where  it  would  be  impossible  to  build  a  small  house.  How- 
ever, in  these  flats  some  of  the  rooms  are  not  well  lighted  and  ventilated, 
and  one  is  dependent  upon  the  janitor  for  many  services  which  are  not 
always  pleasantly  performed,  though  fees  are  constantly  expected.  The 
long  flights  of  stairs  are  a  great  drawback,  because  people  will  not  go  out  as 
much  as  they  should,  on  account  of  the  exhausting  climb  on  their  return. 

The  small  house,  in  country  or  city,  brings  more  healthful 
mental  and  physical  surroundings  than  the  flat.  Perfect  venti- 
lation, light,  sunshine,  and  freedom  from  all  petty  restrictions 
give  a  more  vigorous  tone  to  body  and  mind.  If  the  house  is 
in  the  suburbs  and  there  is  some  land  with  it,  where  a  few 
vegetables  and  flowers  can  be  cultivated,  it  has  an  added  charm 
and  blessing  in  the  form  of  healthful  outdoor  work :  furnace, 
cellar,  and  grounds  for  the  husband's .  share  ;  house,  from 
garret  to  cellar,  for  the  wife's  share.  In  a  flat  a  man  can 
escape  nearly  all  duties  about  the  house,  but  in  the  little  house 
he  must  bear  his  share. 

If  one  lives  in  the  suburbs,  the  time  and  money  spent  in  going  to  and 
from  the  city  is  quite  an  item,  but  the  cheaper  rent  usually  more  than 
balances  the  traveling  expense.  A  person  should  not  pay  over  25  %  of 
income  for  rent.  In  case  a  person  receives  an  income  of  $  1500  or  over, 
and  has  a  savings  bank  deposit  of  about  $  1500,  it  is  usually  better  to 

128 


CONSTRUCTION    OF   A   HOUSE  129 

purchase  a  house  than  to  rent.     Money  may  be  borrowed  from  either  the 
cooperative  bank  or  the  savings  bank. 

The  total  rent  of  a  house  a  year  should  be  at  least  10%  of  the  value  of 
the  house  and  land :  6  %  represents  interest  on  the  investment,  and  4  % 
covers  taxes  and  depreciation.  In  a  flat  the  middle  floor  should  cost 
approximately  10%  more  than  the  first  floor,  and  the  top  10%  less  than 
the  first  floor. 

EXAMPLES 

1.  A  single  house  and  land  cost  $  2800.     What  should  be 
considered  the  rent  per  year  ? 

2.  A  two-family  house  cost  $  5600.      (a)  What  should  be 
the  rent  per  month  ?     (6)  What  should  be  the  rent  of  each  flat  ? 

3.  A  three-family  house  costs  $  6500.     What  should  be  the 
rent  of  each  floor  ? 

4.  A  family  desires    to  build  a  cottage-style,  garnbrel  roof 
house  containing  seven  rooms,  bath,  reception  hall,  cemented 
cellar,  and  small  storage  attic.     It  is  finished  inside  with  North 
Carolina  pine  and  has  hard-pine  floors,  fir  doors,  open  plumb- 
ing, two  coats  of  plaster,  furnace  heat,  and  electric  light.     The 
first  floor  has  three  rooms  and  a  reception  hall.     The  second 
floor  has  three  chambers,  bath,  and  sewing  room  over  the  hall. 
The  architect  finds  that  the  cost  of  materials  in  the  summer 
and  late  fall  varies  as  follows  : 

AMOUNT  SAVED 

ITEM  SUMMER  BY  BUILDING 

IN  THE  FALL 

Mason  work  $200  $1(5.00 

Brick  and  cement  90  7.20 

Lumber  500  60.00 

Finish  125  12.50 

Plumbing  225  22.50 

Heat  (furnace)  100  10.00 

Paint  and  paper  200  20.00 

Plastering  200  16.00 

Electric  wiring  40  3.20 

Electric  light  fixtures  40  4.00 

Labor  (carpenters)  450 

Profit  to  contractor  213  27.52 


130       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

(a)  What  is  the  total  cost  in  each  case?  (6)  What  is  the 
difference  in  per  cent  ?  What  is  the  per  cent  difference  in  each 
item? 

Economy  of  Space 

Many  persons  who  build  houses,  barns,  and  other  buildings 
do  not  understand  the  fundamental  fact  that  there  is  more 
space  in  a  square  building  than  in  a  long  one,  and  that  the 
further  they  depart  from  the  square  form  the  more  their  build- 
ing will  cost  in  proportion  to  its  size.  For  instance,  a  building 
20'  by  20'  has  400  square  feet  of  floor  space  and  requires  80  feet 
of  outside  wall,  while  one  10'  by  40'  will,  with  the  same  floor 
space,  require  100  feet  of  wall.  Accordingly  more  material 
and  work  will  be  required  for  the  longer  one. 

In  many  cases,  of  course,  there  are  objections  to  having  a 
building  square.  The  longer  building,  for  instance,  gives 
more  wall  space  and  more  light,  and  these  may  be  desired 
items.  The  roof  and  floor  items  are  about  the  same  in  either 
case. 

Preparation  of  Wood  for  Building  Purposes 

In  winter  the  forest  trees  are  cut  and  in  the  spring  the  logs  are  floated 
down  the  rivers  to  sawmills,  where  they  are  sawed  into  boards  of  different 
thicknesses.  To  square  the  log,  four  slabs  are  first  sawed  off.  After  these 
slabs  are  off,  the  remainder  is  sawed  into  boards. 

As  soon  as  the  boards  or  planks  are  sawed  from  the  logs,  they  are  piled 
on  prepared  foundations  in  the  open  air  to  season.  Each  layer  is  sepa- 
rated from  the  one  above  by  a  crosspiece,  called  a  strip,  in  order  to  allow 
free  circulation  of  air  about  each  board  to  dry  it  quickly  and  evenly.  If 
lumber  were  piled  up  without  the  strips,  one  board  upon  another,  the 
ends  of  the  pile  would  dry  and  the  center  would  rot.  This  seasoning  or 
drying  out  of  the  sap  usually  requires  several  months. 

Wood  that  is  to  be  subject  to  a  warm  atmosphere  has  to  be  artificially 
dried.  This  artificially  dried  or  kiln-dried  lumber  has  to  be  dried  to  a 
point  in  excess  of  that  of  the  atmosphere  in  which  it  is  to  be  placed  after 
being  removed  from  the  kiln.  This  process  of  drying  must  be  done  grad- 
ually and  evenly  or  the  boards  may  warp  and  then  be  unmarketable. 


CONSTRUCTION   OF   A   HOUSE  131 

Definitions 

Board  Measure.  —  A  board  one  inch  or  less  in  thickness  is  said 
to  have  as  many  board  feet  as  there  are  square  feet  in  its  surface. 
If  it  is  more  than  one  inch  thick,  the  number  of  board  feet  is 
found  by  multiplying  the  number  of  square  feet  in  its  surface 
by  its  thickness  measured  in  inches  and  fractions  of  an  inch. 

The  number  of  board  feet  —  length  (in  feet]  x  width  (in  feet}  x  thick- 
ness (in  inches'). 

Board  measure  is  used  for  plank  measure.  A  plank  2"  thick,  10"  wide, 
and  15'  long,  contains  twice  as  many  square  feet  (board  measure)  as  a 
board  1"  thick  of  the  same  width  and  length. 

Boards  are  sold  at  a  certain  price  per  hundred  (C)  or  per  thousand  (M) 
board  feet. 

The  term  lumber  is  applied  to  pieces  not  more  than  four  inches  thick ; 
timber  to  pieces  more  than  four  inches  thick ;  but  a  large  amount  taken 
together  often  goes  by  the  general  name  of  lumber.  A  piece  of  lumber 
less  than  an  inch  and  a  half  thick  is  called  a  board  and  a  piece  from  one 
inch  and  a  half  to  four  inches  thick  is  called  a  plank. 

Rough  Stock  is  lumber  the  surface  of  which  has  not  been  dressed  or 
planed. 

The  standard  lengths  of  pieces  of  lumber  are  10,  12, 14, 16,  18  feet,  etc. 

EXAMPLES 

1.  How  many  board  feet  in  a  board  1  in.  thick,  15  in.  wide, 
and  15  ft.  long  ? 

2.  How  many  board  feet  of  2-inch  planking  will  it  take  to 
make  a  walk  3  feet  wide  and  4  feet  long  ? 

3.  A  plank  19'  long,  3"  thick,  10"  wide  at  one  end  and  12" 
wide  at  the  other,  contains  how  many  board  feet  ? 

4.  Find  the  cost  of  7  2-inch  planks  12  ft.  long,  16  in.  wide 
at  one  end,  and  12  in.  at  the  other,  at  $  0.08  a  board  foot. 

5.  At  $  12  per  M,  what  will  be  the  cost  of  2-inch  plank  for 
a  3  ft.  6  in.  sidewalk  on  the  street  sides  of  a  rectangular  corner 
lot  56  ft.  by  106  ft.  6  in.  ? 


132       VOCATIONAL   MATHEMATICS   FOR   GIRLS 


Frame  and  Roof 

After  the  excavation  is  finished  and  the  foundation  laid,  the  construc- 
tion of  the  building  itself  is  begun.  On  the  top  of  the  foundation  a  large 
timber  called  a  sill  is  placed.  The  timbers  running  at  right  angles  to  the 
front  sill  are  called  side  sills.  The  sills  are  joined  at  the  corners  by  a 
half -lap  joint  and  held  together  by  spikes. 


a.  Outside  studding 
6.  Rafters 

c.  Plates 

d.  Ceiling  joists 


de.  Second-floor  joists  i. 

def.  First-floor  joists  j. 

g.  Girder  or  cross  sill  k. 

h.  Sills  /. 


Sheathing 
Partition  studs 
Partition  heads 
Piers 


The  walls  of  the  building  are  framed  by  placing  corner  posts  4"  by  6" 
on  the  four  corners.  Between  these  corner  posts  there  are  placed  smaller 
timbers  called  studding,  2"  by  4",  16"  apart.  Later  the  laths,  4'  long,  are 
nailed  to  this  studding.  The  upright  timbers  are  often  mortised  into  the 
sills  at  the  bottom.  When  these  uprights  are  all  in  position,  a  timber,  called 
a  plate,  is  placed  on  the  top  of  them  and  they  are  spiked  together. 

On  the  top  of  the  plate  is  placed  the  roof.  The  principal  timbers  of 
the  roof  are  the  rafters.  Different  roofs  have  a  different  pitch  or  slope  — 
that  is,  form  different  angles  with  the  plate.  To  obtain  the  desired  pitch 
the  carpenter  uses  the  steel  square. 


CONSTRUCTION   OF   A   HOUSE  133 

A  roof  with  one  half  pitch  means  that  the  height  of  the  ridge  of  the 
roof  above  the  level  of  the  plate  is  equal  to  one  half  the  width  of  the 
building. 

This  illustrates  a  roof  with  one-half  pitch. 


EXAMPLES 

Give  the  height  of  the  ridge  of  the  roof  above  the  level  of 
the  plate  of  the  following  building : 

PITCH  WIDTH  OF  BUILDING 

1.  One-half  32' 

2.  One-fourth  40' 

3.  One-third  36' 

4.  One-sixth  48' 

Building  Materials 

Besides  wood  many  materials  enter  into  the  construction  of 
buildings ;  among  these  are  mortar,  cement,  stone,  bricks, 
marble,  slate,  etc. 

Mortar  is  a  paste  formed  by  mixing  lime  with  water  and  sand  in  the 
correct  proportions.  (Common  mortar  is  generally  made  of  1  part  of 
lime  to  5  parts  of  sand.)  It  is  used  to  hold  bricks,  etc.,  together,  and 
when  stones  or  bricks  are  covered  with  this  paste  and  placed  together, 
the  moisture  in  the  mortar  evaporates  and  the  mixture  "  sets  "  by  the 
absorption  of  the  carbon  dioxide  from  the  air.  Mortar  is  strengthened 
by  adding  cow's  hair  when  it  is  used  to  plaster  a  house  ;  in  such  mortar 
there  is  sometimes  half  as  much  lime  as  sand. 

Plaster  is  a  mixture  of  a  cheap  grade  of  gypsum  (calcium  sulphate), 
sand,  and  hair.  When  the  plaster  is  mixed  with  water,  the  water  com- 
bines with  the  gypsum  and  the  minute  crystals  in  forming  interlace  and 
cause  the  plaster  to  "  set." 

When  masons  plaster  a  house,  they  estimate  the  amount  of 
work  to  be  done  by  the  square  yard.  Nearly  all  masons  use 
the  following  rule :  Calculate  the  total  area  of  walls  and  ceil- 


134       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

ings  and  deduct  from  this  total  area  one-half  the  area  of  open- 
ings such  as  doors  and  windows.  A  bushel  of  mortar  will 
cover  about  3  sq.  yd.  with  two  coats. 

EXAMPLE.  —  How  many  square  yards  of  plastering  are  nec- 
essary to  plaster  walls  and  ceiling  of  a  room  28'  by  32'  and  12' 
high? 

Areas  of  the  front  and  back  walls  are  28  x  12  x    2  =    672  sq.  ft. 
Areas  of  the  side  walls  are  32  x  12  x    2  =    768  sq.  ft. 

Area  of  the  ceiling  is  28  x  32  =    896  sq.  ft. 

"2336  sq.  ft. 
2336  sq.  ft.  =  **-£&  sq.  yd.  =  259f  sq.  yd. 

260  sq.  yd.    Ans. 

EXAMPLES 

1.  What  will  it  cost  to  plaster  a  wall  10  ft.  by  13  ft.  at 
$  0.30  per  square  yard  ? 

2.  What  will  it  cost  to  plaster  a  room  28'  6"  by  32'  4"  and 
9'  6"  high,  at  29  cents  a  square  yard,  if  one-half  its  area  is 
allowed  for  openings  and  there  are  two  doors  8'  by  3^'  and 
three  windows  6'  by  3'  3"  ? 

3.  What  will  it  cost  to  plaster  an  attic  22'  4"  by  16'  8"  and 
9'  4"  high,  at  a  cost  of  32  cents  a  square  yard  ? 

Bricks  used  in  Building 

Brickwork  is  estimated  by  the  thousand,  and  for  various 
thicknesses  of  wall  the  number  required  is  as  follows : 

8^-inch  wall,  or  1  brick  in  thickness,  14  bricks  per  superficial  foot. 
12f-inch  wall,  or  \\  bricks  in  thickness,  21  bricks  per  superficial  foot. 
17-inch  wall,  or  2  bricks  in  thickness,  28  bricks  per  superficial  foot. 
21^-inch  wall,  or  2|  bricks  in  thickness,  35  bricks  per  superficial  foot. 

•  EXAMPLES 

From  the  above  table  solve  the  following  examples : 
1.    How  much  brickwork  is  in  a  17"  wall  (that  is,  2  bricks 
in  thickness)  180'  long  by  6'  high  ? 


CONSTRUCTION   OF  A   HOUSE  135 

2.  How  many  bricks  in  an  8J"  wall,  164'  6"  long  by  6'  4"  ? 

3.  How  many  bricks  in  a  17"  wall,  48'  3"  long  by  4'  8"  ? 

4.  How  many  bricks  in  a  211"  wall,  36'  4"  long  by  3'  6"  ? 

5.  How  many  bricks  in  a  12f"  wall,  38'  3"  long  by  4'  2"? 

6.  At  $  19  per  thousand  find  the  cost  of  bricks  for  a  build- 
ing 48'  long,  31'  wide,  23'  high,  with  walls  12f"  thick.     There 
are  5  windows  (V  x  3')  and  4  doors  (4'  x  81'). 

To  estimate  the  number  of  bricks  in  a  wall  it  is  customary 
to  find  the  number  of  cubic  feet  and  then  multiply  by  22, 
which  is  the  number  of  bricks  in  a  cubic  foot  with  mortar. 

7.  How  many  bricks  are  necessary  to  build  a  partition  wall 
36'  long,  22'  wide,  and  18"  thick  ? 

8.  How  many  bricks  will   be  required  for  a  wall   28'  6" 
long,  16'  8"  wide,  and  6'  5"  high? 

9.  How  many  cubic  yards  of  masonry  will  be  necessary  to 
build  a  wall  18'  4"  long  and  12'  2"  wide  and  4"  thick? 

10.  At  $  19  per  thousand,  how  much  will  the  bricks  cost  to 
build  an  8^",  or  one-brick  wall,  28'  4"  long  and  8'  3"  high  ? 

11.  At  $  20.50  per  thousand,  how  much  will  the  bricks  cost 
to  build  a  12f "  wall,  52'  6"  long  and  14'  8"  high  ? 

12.  A  house  is  45'  x  34'  x  18',  the  walls  are  1  foot  thick, 
the  windows  and  doors  occupy  368  cu.  ft. ;  how  many  bricks 
will  be  required  to  build  the  house  ? 

13.  What  will  it  cost  to  lay  250,000  bricks,  if  the  cost  per 
thousand  is  $  8.90  for  the  bricks  ;  $  3  for  mortar  ;  laying,  $  8  ; 
and  staging,  $  1.25  ? 

Stonework 

Stonework,  like  brickwork,  is  measured  by  the  cubic  foot 
or  by  the  perch  (161'  x  !£'  X  1')  or  cord.  Practical  men  usu- 
ally consider  24  cubic  feet  to  the  perch  and  120  cubic  feet  to 
the  cord.  The  cord  and  perch  are  not  much  used, 


136       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

The  usual  way  is  to  measure  the  distance  around  the  cellar  on  the  out- 
side for  the  length.  This  includes  the  corners  twice,  but  owing  to  the 
extra  work  in  making  corners  this  is  considered  proper.  No  allowance  is 
made  for  openings  unless  they  are  very  large,  when  one-half  is  deducted. 

The  four  walls  may  be  considered  as  one  wall  with,  the  same 
height. 

EXAMPLE.  —  If  the  outside  dimensions  of  a  wall  are  44'  by 
31',  10'  6"  high  and  8"  thick,  find  the  number  of  cubic  feet. 

44  2r 

?!  %          2 

'5  m  x  —  x  4-  =  1050  cu.  ft.    Ans. 

150  ft.  length.  £ 

Cement 

Some  buildings  have  their  columns  and  beams  made  of 
concrete.  Wooden  forms  are  first  set  up  and  the  concrete  is 
poured  into  them.  The  concrete  consists  of  Portland  cement, 
sand,  and  broken  stone,  usually  in  the  proportion  of  1  part 
cement  to  2  parts  sand  and  4  parts  stone.  The  average  weight 
of  this  mixture  is  150  pounds  per  cubic  foot.  After  the  con- 
crete has  "  set,"  the  wooden  boxes  or  forms  are  removed. 

Within  a  few  years  twisted  steel  rods  have  been  placed  in  the  forms 
and  the  concrete  poured  around  them.  This  is  called  reenforced  con- 
crete and  makes  a  stronger  and  safer  combination  than  the  whole  concrete. 
It  is  used  in  walls,  sewers,  and  arches.  It  takes  a  long  time  for  the  con- 
crete to  reach  its  highest  compressive  and  tensile  strength. 

Cement  is  also  used  for  walls  and  floors  where  a  waterproof  surface  is 
desired.  When  the  cement  "sets,"  it  forms  a  layer  like  stone,  through 
which  water  cannot  pass.  If  the  cement  is  inferior  or  not  properly  made, 
it  will  not  be  waterproof  and  water  will  pass  through  it  and  in  time 
destroy  it. 

EXAMPLES 

1.  If  one  bag  (cubic  foot)  of  cement  and  one  bag  of  sand 
will  cover  2-|  sq.  yd.  one  inch  thick,  how  many  bags  of  cement 
and  of  sand  will  be  required  to  cover  30  sq.  yd.  2£"  thick  ? 


CONSTRUCTION    OF   A   HOUSE  137 

2.  How  many  bags  of  cement  and  of  sand  will  be  required 
to  lay  a  foundation  V  thick  on  a  sidewalk  20'  by  8'  ? 

3.  How  many  bags  of  cement  and  of  sand  will  it  take  to 
cover  a  walk,  34'  by  8'  6",  I"  thick  ? 

4.  If  one  bag  of  cement  and  two  of  sand  will  cover  5^  sq.  yd. 
f"  thick,  how  much  of  each  will  it  take  to  cover  128  sq.  ft.  ? 

5.  How  much  of  a  mixture  of  one  part  cement,  two  parts 
sand,  and  four  parts  cracked  stone  will  be  needed  to  cover  a 
floor  28'  by  32'  and  8"  deep  ?    How  much  of  each  will  be  used  ? 

Shingles 

Shingles  for  roofs  are  figured  as  being  16"  by  4"  and  are 
sold  by  the  thousand.  The  widths  vary  from  2"  upward. 
They  are  put  in  bundles  of  250  each.  When  shingles  are  laid 
on  the  roof  of  a  building,  they  overlap  so  that  only  part  of 
each  is  exposed  to  the  weather. 

EXAMPLES 

1.  How  much  will  it  cost  for  shingles   to   shingle   a  roof 
50  ft.  by  40  ft.,  if  1000  shingles  are  allowed  for  125  sq.  ft. 
and  the  shingles  cost  $  1.18  per  bundle  ? 

2.  Find  the  cost  of  shingling  a  roof  38  ft.  by  74  ft.,  4"  to 
the  weather,  if  the  shingles  cost  $  1.47  a  bundle,  and  a  pound 
and  a  half  of  cut  nails  at  6  cents  a  pound  are  used  with  each 
bundle. 

3.  How  many  shingles  would  be  needed  for  a  roof  having 
four  sides,  two  in  the  shape  of  a  trapezoid  with  bases  30  ft.  and 
10  ft.,  and  altitude  15  ft.,  and  two  (front  and  back)   in  the 
shape   of  a   triangle  with   base   20   ft.  and   altitude   15   ft.? 
(1000  shingles  will  cover  120  sq.  ft.) 

Slate  Roofing 

In  order  to  make  the  exterior  of  a  house  fireproof  the  roof 
should  be  tile  or  slate.  Slates  make  a  good-looking  and  durable 


138       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

roof.     They  are  put  on,  like  shingles,  with  nails.     Estimates 
for  slate  rooting  are  made  on  100  sq.  ft.  of  the  roof.1 

The  following  are  typical  data  for  building  a  slate  roof : 

A  square  of  No.  10  x  20  Monson  slate  costs  about  $  8.35. 
Two  pounds  of  galvanized  nails  cost  $0.16  per  pound. 
Labor,  $  3  per  square. 
Tar  paper,  at  2f  cents  per  pound,  1|  Ib.  per  square  yard. 

EXAMPLES 

Using  the  above  data,  give  the  cost  of  making  slate  roofs 
for  the  following  : 

1.  What  is  the  cost  of  laying  a  square  of  slate  ? 

2.  What  is  the  cost  of  laying  slate  on  a  roof  112'  by  44'  ? 

3.  What  is  the  cost  of  laying  slate  on  a  roof  156'  by  64'? 

4.  What  is  the  cost  of  laying  slate  on  a  roof  118'  by  52'  ? 

5.  What  is  the  cost  of  laying  slate  on  a  roof  284'  by  78'  ? 

Clapboards 

Clapboards  are  used  to  cover  the  outside  walls  of  frame 
buildings.  Most  clapboards  are  4'  long  and  6"  wide.  They 
are  sold  in  bundles  of  twenty-five.  Three  bundles  will  cover 
100  square  feet  if  they  are  laid  4"  to  the  weather. 

To  find  the  number  of  clapboards  required  to  cover  a  given 
area,  find  the  area  in  square  feet  and  divide  by  1-J.  Allowance 
may  be  made  for  openings  by  deducting  from  area. 

EXAMPLES 

1.  How  many  clapboards  will  be  required  to  cover  an  area 
of  40  ft.  by  30  ft.? 

2.  How  many  clapboards  will  be  necessary  to  cover  an  area 
of  38'  by  42'  if  56  sq.  ft.  are  allowed  for  doors  and  windows  ? 

3.  How  many  clapboards  will  a  barn  60  ft.  by  50  ft.  require 
if  10  %  is  allowed  for  openings  and  the  distance  from  founda- 
tion to  the  plate  is  17  ft.  and  the  gable  10  ft.  high  ? 

1  Called  a  square. 


CONSTRUCTION   OF   A   HOUSE  139 

Flooring 

Most  floors  in  houses  are  made  of  oak,  maple,  birch,  or  pine. 
This  flooring  is  grooved  so  that  the  boards  fit  closely  together 
without  cracks  between  them. 


The   accompanying   figure  shows   the  ends  of    i=] c; c L^ 

pieces  of  matched  flooring.     Matched  boards  are 

also  used  for  ceilings  and  walls.  In  estimating  for  matched  flooring 
enough  stock  must  be  added  to  make  up  for  what  is  cut  away  from  the 
width  in  matching.  This  amount  varies  from  \"  to  |"  on  each  board  ac- 
cording to  its  size.  Some  is  also  wasted  in  squaring  ends,  cutting  up,  and 
fitting  to  exact  lengths.  A  common  floor  is  made  of  unmatched  boards 
and  is  usually  used  as  an  under  floor.  Not  more  than  \"  per  board  is 
allowed  for  waste. 

EXAMPLE.  —  A  room  12  ft.  square  is  to  have  a  floor  laid  of 
unmatched  boards  I!"  wide ;  one-third  is  to  be  added  for  waste. 
What  is  the  number  of  square  feet  in  the  floor  ?  What  is  the 
number  of  board  feet  required  for  laying  the  floor  ? 

12  x  12  =  144  sq.  ft.  =  area.  144  x  \  =    48 

144.     Ans.  144 

192  board  measure  for 

unmatched  floor. 
192.     Ans. 

EXAMPLES 

1.  How  much  -J  in.  matched  flooring  3"  wide  will  be  re- 
quired to  lay  a  floor  16  ft.  by  18  ft.  ?     One-fourth  more  is  al- 
lowed for  matching  and  3  °/0  for  squaring  ends. 

2.  How  much  hard  pine  matched  flooring  -|"  thick  and  1^" 
wide  will  be  required  for  a  floor  13'  6"  x  14'  10"  ?     Allow  \  for 
matching  and  add  4  %  for  waste. 

3.  An  office  floor  is  10'  6"  wide  at  one  end  and  9'  6"  wide  at 
the  other  (trapezoid)  and  11' 7"  long.     What  will  the  material 
cost  for  an  unmatched  maple  floor  -J-"  thick  and  1?"  wide  at 
$  60  per  M,  if  4  sq.  ft.  are  allowed  for  waste  ? 


140       VOCATIONAL   MATHEMATICS   FOR   GIRLS 


4.  How  many  square  feet  of  sheathing  are  required  for  the 
outside,  including  the  top,  of  a  freight  car  34'  long,  8'  wide, 
and  7-J-'  high,  if  37-^-%  covers  all  allowances  ? 

5.  In  a  room  50'  long  and  20'  wide  flooring  is  to  be  laid  ; 
how  many  feet  (board  measure)  will  be  required  if  the  stock 
is  y  X  3"  and  \  allowance  for  waste  is  made  ? 

Stairs 

The  perpendicular  distance  between  two  floors  of  a  building 
is  called  the  rise  of  a  flight  of  stairs.  The  width  of  all  the 

steps  is  called  the  run. 
The  perpendicular  dis- 
tance between  steps  is 
called  the  width  of  risers. 
Nosing  is  the  slight  pro- 
jection on  the  front  of 
each  step.  The  board  on 
each  step  is  the  tread. 

To  find  the  number  of 
stairs  necessary  to  reach 
from  one  floor  to  another  : 
Measure    the    rise    first. 
STAIRS  Divide  this  by  8  inches, 

which  is  the  most  comfortable  riser  for  stairs.  The  run  should 
be  81-  inches  or  more  to  allow  for  a  tread  of  9|  inches  with 
a  nosing  of  1  \  inches. 

EXAMPLE.  —  How  many  steps  will  be  required,  and  what 
will  be  the  riser,  if  the  distance  between  floors  is  118  inches  ? 

118  -f-    8  =  14|  or  15  steps. 

118  -r- 15  =  7-J-f  inches  each  riser.     Ans. 

EXAMPLES 

1.  How  many  steps  will  be  required,  and  what  will  be  the 
riser,  (a)  if  the  distance  between  floors  is  8'  ?  (6)  If  the  dis- 
tance is  9  feet  ? 


CONSTRUCTION    OF   A   HOUSE  141 

2.  How  many  steps  will  be  required,  and  what  will  be  the 
riser,  (a)  if  the  distance  between  floors  is  12'  ?  (b)  If  the  dis- 
tance is  8' 8"? 

Lathing 

Laths  are  thin  pieces  of  wood,  4  ft.  long  and  11  in.  wide, 
upon  which  the  plastering  of  a  house  is  laid.  They  are  usu- 
ally put  up  in  bundles  of  one  hundred.  They  are  nailed  J  in. 
apart  and  fifty  will  cover  about  30  sq.  ft. 

EXAMPLES 

1.  At  30  cents  per  square  yard  what  will  it  cost  to  lath  and 
plaster  a  wall  12  ft.  by  15  ft.  ? 

2.  At  45  cents  per  square  yard  what  will  it  cost  to  lath  and 
plaster  a  wall  18  ft.  by  16  ft.  ? 

3.  What  will  it  cost  to  lath  and  plaster  a  room  (including 
walls  and  ceiling)  16  ft.  square  by  12  ft.  high,  allowing  34  sq.  ft. 
for  windows  and  doors,  at  40  cents  per  square  yard  ? 

4.  What  will  it  cost  to  lath  and  plaster  the  following  rooms 
at  411  cents  per  square  yard  ? 

a.  16' x  14' xir  high  with  a  door    8'  x2£' and  2  windows  2£'  x  5'. 
6.  18' x  15' xir  high  with  a  door  10' X  3'  and  4  windows  2|'  X  5'. 

c.  20'  x  18'  x  12'  high  with  a  door  11'  x  3'  and  4  windows  2f  x  4'. 

d.  28'  x  32'  x  16'  high  with  a  door  10'  x  3'  and  4  windows  3'    x5'. 

e.  28' x  30' x  15' high  with  a  door  10' x  3'  and  3  windows  3'    x5'. 

Painting 

Paint,  which  is  composed  of  dry  coloring  matter  or  pigment  mixed 
with  oil,  drier,  etc.,  is  applied  to  the  surface  of  wood  by  means  of  a 
brush  to  preserve  the  wood.  The  paint  must  be  composed  of  materials 
which  will  render  it  impervious  to  water,  or  rain  would  wash  it  from  the 
exterior  of  houses.  It  should  thoroughly  conceal  the  surface  to  which 
it  is  applied.  The  unit  of  painting  is  one  square  yard.  In  painting 
wooden  houses  two  coats  are  usually  applied. 


142       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

It  is  often  estimated  that  one  pound  of  paint  will  cover  4  sq.  yd.  for 
the  first  coat  and  6  sq.  yd.  for  the  second  coat.  Some  allowance  is  made 
for  openings  ;  usually  about  one-half  the  area  of  openings  is  deducted, 
for  considerable  paint  is  used  in  painting  around  them. 

TABLE 

1  gallon  of  paint  will  cover  on  concrete  .     .     .  300  to  375  superficial  feet 

1  gallon  oi'  paint  will  cover  on  stone  or  brick 

work 190  to  225  superficial  feet 

1  gallon  of  paint  will  cover  on  wood  ....  375  to  525  superficial  feet 

1  gallon  of  paint  will  cover  on  well-painted  sur- 
face or  iron 600  superficial  feet 

1  gallon  of  tar  will  cover  on  first  coat     ...  90  superficial  feet 

1  gallon  of  tar  will  cover  on  second  coat      .     .  160  superficial  feet 

EXAMPLES 

1.  How  many  gallons  .of  paint  will  it  take  to  paint  a  fence 
6'  high,  and  50'  long,  if  one  gallon  of   paint  is  required  for 
every  350  sq.  ft.? 

2.  What  will  be  the  cost  of  varnishing  a  floor  22'  long  and 
16'  wide,  if  it  tak^s  a  pint  of  varnish  for  every  four  square 
yards  of  flooring  and  the  varnish  costs  $2.65  per  gallon  ? 

3.  What  will  it  cost  to  paint  a  ceiling  36'  by  29'  at  21  cents 
per  square  yard  ? 

4.  What  will  be  the  cost  of  painting  a  house  which  is  52' 
long,  31'  wide,  21'  high,  if  it  takes  one  gallon  of  paint  to  cover 
300  sq.  ft.  and  the  paint  costs  $  1.65  per  gallon  ?     (House  has 
a  flat  roof.) 

Papering 

Wall  paper  is  18"  wide  and  may  be  bought  in  single  rolls 
8  yards  long  or  double  rolls  16  yards  long.  When  you  get  a 
price  on  paper,  be  sure  that  you  know  whether  it  is  by  the 
single  or  double  roll.  It  is  usually  more  economical  to  buy  a 
double  roll.  There  is  considerable  waste  in  cutting  and  match- 
ing paper,  hence  it  is  difficult  to  estimate  the  exact  amount. 


CONSTRUCTION    OF   A   HOUSE  143 

A  fraction  of  a  roll  is  not  sold,  —  there  are  various  rules  pro- 
vided. The  border,  called  frieze,  is  usually  sold  by  the  yard. 

Find  the  perimeter  of  the  room  in  feet,  and  divide  this  by 
the  width  of  the  paper  (which  is  18"  or  li').  The  quotient 
obtained  equals  the  number  of  strips  of  paper  required.  Then 
divide  the  length  of  the  roll  by  the  height  of  the  room  in  order 
to  obtain  the  number  of  strips  in  the  roll.  The  number  of 
rolls  required  is  found  by  dividing  the  strips  in  the  room  by  the 
strips  in  the  roll. 

Another  rule  is :  Find  the  perimeter  of  the  room  in  yards, 
multiply  that  by  2,  and  you  have  the  number  of  strips.  Find 
the  length  of  each  strip.  How  many  whole  strips  can  you  cut 
from  a  double  roll  ?  How  many  rolls  will  it  take  ?  To  allow 
for  doors  and  windows  deduct  1  yard  from  the  perimeter  for 
each  window  and  each  door. 

EXAMPLES 

1.  A  paper  hanger  is  asked  to  paper  a  square  room  18'  by 
18'  with  a  door  and  three  windows.     The  door  is  3'  by  7'  and 
the  windows  2'  by  4'.     How  many  double  rolls  of  paper  will 
he  use  ?     (Consider  all  rooms  9'  high.) 

2.  How  much  paper  will  be  required  to  paper  a  room  18' 
by  14'  ? 

3.  How   much   paper   will   be   required   to   paper   a   room 
18'  6"  by  16'  4"  with  2  doors  and  2  windows  ? 

4.  How   much   will    it   cost   to   paper  a    room    19'  6"   by 
16'   4"  with  2  doors  and  2  windows.     The  paper  costs  49^ 
a  roll  to  place  it  on  the  wall. 

Taxes 

Find  out  where  the  money  comes  from  to  support  the 
schools,  police,  library,  etc.  in  your  city  or  town.  How  is  it 
obtained  ?  What  is  real  estate  ?  What  is  personal  property  ? 
What  is  a  poll  tax  ?  A  tax  is  the  sum  of  money  assessed  on 
persons  and  property  to  defray  the  expenses  of  the  community. 


144       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

The  tax  rate  is  usually  expressed  as  so  many  dollars  per 
thousand  of  valuation,  generally  between  $  10  and  $  20.  In 
some  places  it  is  expressed  as  a  certain  number  of  mills  on  $  1 
or  cents  on  $  100. 

The  tax  rate,  or  the  amount  on  each  thousand  dollars  of 
property,  is  determined  by  dividing  the  whole  tax  by  the  num- 
ber of  thousand  dollars  of  taxable  property  in  the  community. 
To  illustrate : 

In  a  certain  community  the  whole  tax  is  $1,942,409.73. 
The  taxable  property  is  $  97,945,162.00. 

$1,942,409.73  983 

97,945 

EXAMPLES 

1.  If  the  tax  rate  is  $  21.85,  what  are  the  taxes  paid  by  a 
family  of  women  owning  property  worth  $  16,000  ? 

2.  What  is  the  tax  on  $  34,697  in  your  town  or  city  ? 

3.  A  man  owns  real  estate  worth  $  84,313,  and  has  personal 
property  worth  $  16,584.    What  is  his  tax  bill,  if  the  tax  rate 
is  $  1.75  per  hundred  and  a  poll  tax  is  $  2  ? 

4.  A  dwelling  house  is  valued  at  $  8500  and  the  tax  rate 
is  $  17.52  per  thousand.     What  is  the  tax  ? 

5.  Wrhat  is  the  tax  on  a  house  valued  at  $  3500,  if  the  tax 
rate  is  $  23.45  ? 

6.  The  taxable  property  of  a  city  is  $  97,945,162.00 ;  and  the 
expenses  (taxes)  necessary  to  run  the  city  are  $  1,900,136.14. 
Obtain  the  tax  rate. 

United  States  Revenue 

The  town  or  city  derives  revenue  from  taxes  levied  on  real 
and  personal  property.  The  county  and  state  derive  part  of 
their  revenue  from  a  tax  imposed  upon  the  towns  and  cities. 
The  United  States  government  derives  a  great  part  of  its  rev- 


CONSTRUCTION    OF   A   HOUSE  145 

enue  from  a  tax  placed  on  tobacco  and  liquor  sold  within  its 
boundaries  and  from  a  tax,  called  customs  duties,  imposed  upon 
articles  imported  from  other  countries. 

Some  articles  are  admitted  into  the  country  free;  these  are  said  to 
be  on  the  free  list.  The  others  are  subject  to  one  or  both  of  the  follow- 
ing duties  :  a  duty  placed  on  the  weight  or  quantity  of  an  article  without 
regard  to  value  (called  specific  duty),  or  a  duty  based  upon  the  value  of 
the  article  (expressed  in  per  cent  and  called  ad  valorem  duty). 

When  goods  are  received  into  this  country,  they  are  examined  by  an 
officer  (called  a  customs  officer).  The  goods  are  accompanied  by  a 
written  statement  of  the  quantity  and  value  (called  manifest  or  invoice). 

Sometimes  the  goods  are  liquid,  and  in  this  case  the  weight  of  the  bar- 
rel (called  tare)  must  be  subtracted  from  the  total  weight  to  obtain  the 
net  weight  on  which  duty  is  imposed. 

In  case  bottles  are  broken  and  liquids  have  escaped,  due  allowance 
must  be  made  before  imposing  duty.  This  is  called  leakage  or  breakage. 

EXAMPLES 

1.  What  is  the  duty  on  bronze  worth  $  8760  at  45  %  ? 

2.  What  is  the  duty  on  goods  valued  at  $  3115  at  35  %  ? 

3.  What  is  the  duty  on  3843  sq.   ft.  of  plate  glass,  duty 
$  0.09  per  square  foot  ? 

4.  What  is  the  duty  on  jewelry  valued  at  $  8376  at  40  %  ? 

5.  What   is  the   duty  on   cotton   handkerchiefs  valued   at 
$  834  at  45  %  ? 

6.  What  is  the  duty  on  woolen  knit  goods  valued  at  $  1643, 
41  cts.  per  pound  plus  50  °/0  ? 

7.  What  is  the  duty  on  rugs  (Brussels),  120  yards,  27"  wide, 
invoiced  at  $  1.80  a  yard,  at  29  cts.  per  square  yard  and  45  % 
ad  valorem  ? 


CHAPTER  VII 
COST  OF  FURNISHING  A  HOUSE 

WHEN  about  to  furnish  a  house,  one  of  the  first  things  to 
consider  is  the  amount  of  money  to  be  devoted  to  the  purpose. 
This  amount  should  depend  on  the  income.  A  person  with 
a  salary  of  $  1000  a  year  should  have  saved  at  least  $  250 
toward  the  equipment  of  his  home  before  starting  house- 
keeping. This  is  sufficient  to  purchase  the  essentials  of  a 
simply  furnished  apartment  or  small  house. 

After  one  has  lived  in  the  house  for  a  short  time,  it  will  be  easy 
to  study  the  possibilities  and  necessities  of  each  room,  and  as  time, 
opportunity,  and  money  permit,  one  can  add  such  other  things  as  are 
needed.  In  this  way  the  purchase  of  undesirable  and  inharmonious 
articles  may  be  avoided. 

There  are  many  different  styles  and  grades  of  furniture.  The  cost 
depends  upon  the  kind  of  wood  used,  and  the  care  with  which  it  is  put 
together  and  finished.  The  most  inexpensive  furniture  is  not  the 
cheapest  in  the  end.  It  is  made  of  inferior  wood  and  with  so  little  care 
that  it  is  neither  durable  nor  attractive.  The  medium  grades  are  gen- 
erally made  of  birch,  oak,  or  willow,  are  durable,  and  may  be  found 
in  styles  that  are  permanently  satisfactory.  The  best  grades  are  made  of 
mahogany  and  other  expensive  woods,  and  those  whose  income  consists 
only  of  wages  or  a  salary  cannot  usually  afford  to  buy  more  than  a  few 
pieces  of  this  kind. 

Furniture  that  is  well  made,  of  good  material,  and  free  from  striking 
peculiarities  of  design  and  of  decoration  is  chosen  by  all  people  of  good 
taste  and  good  judgment. 

Furnishing  the  Hall 

The  only  furniture  necessary  for  the  vestibule  is  a  rack  for  umbrellas. 
The  walls  should  be  painted  with  oil  paint  in  some  warm  color,  and  the 
floor  should  be  tiled  or  covered  with  inlaid  linoleum  in  tile  or  mosaic 

146 


COST    OF   FURNISHING   A   HOUSE 


147 


design.  If  the  vestibule  serves  also  as  the  only  hall,  it  should  contain  a 
rug,  a  small  table  or  chair,  and  a  mirror.  A  panel  of  filet  lace  is  suitable 
to  use  across  the  glass  in  the  front  door. 

Through  the  front  door  one  gets  one's  first  impression  of  the  occupants 
of  the  house.  The  furnishings  of  the  hall  should  therefore  be  carefully 
chosen.  It  is  a  passageway  rather  than  a  room,  and  requires  very  little 
furniture.  The  walls  may  be  done  in  a  landscape  paper,  if  one  wishes  to 
make  the  room  appear  larger,  or  in  plain  colonial  yellow,  if  a  bright  effect 
is  desired.  If  the  size  of  the  hall  will  permit,  it  is  best  to  furnish  it  as  a 
reception  room;  it  may  be  made  an  attractive  meeting  place  for  the 
family  and  friends  ;  but  if  it  is  one  of  the  narrow  passages  so  often  found 
in  city  houses,  one  must  be  content  with  the  regulation  hall  stand,  or  a 
mirror  and  a  narrow  table,  and  possibly  one  chair. 


PRICE  LIST  OF  HALL  FURNITURE 


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Umbrella  rack  . 

§  1.25 

$6.00 

§7.25 

68.50 

$10.00 

§5.00 

§7.60 

Table   .... 

3.75 

6.75 

8.25 

9.75 

20.00 

10.00 

37.50 

Mirror       .     . 

3.00 

3.00 

3.40 

3.75 

30.00 

7.50 

Straight  chair    . 

2.75 

4.50 

5.50 

6.60 

25.00 

6.50 

8.00 

Chest  .... 

13.50  i  13.50 

16.50 

19.50 

50.00 

40.00 

Sofa     .... 

50.00 

35.00 

16.00 

Tall  clock      .     . 

60.00 

60.00 

150.00 

75.00 

Settle  .... 

18.00 

18.00 

22.50 

27.00 

32.00 

32.00 

21.00 

Telephone  stand 

6.75 

6.75 

8.25 

9.75 

10.60 

5.50 

15.00 

Clothes  rack 

3.50 

3.50 

4.15 

4.90 

5.00 

7.00 

8.26 

EXAMPLES 

1.   What   is  the  complete  cost  of   furnishing  a   hall  with 
willow  furniture  ? 


148       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

2.  Compare  the  cost  of  furnishing  a  hall  with  mahogany 
or  birch. 

3.  If  a  family  receives  an  income  of    $  1400  a  year  and 
lives  in  a  single  cottage  house,  what  kind  of  furniture  should 
be  selected?     What  should  the  cost  not  exceed  for  the  hall 
furniture  ? 

4.  A  hall  was  furnished  with  the  following  articles.     What 
did  it  cost  ?     What  kind  of  furniture  was  probably  purchased  ? 

Seat,  $11.85  Rug,  $9.85 

Mirror,  $  2.15  China  umbrella  stand,  $  2.10 

Table,  $2.20  Table  cover  (one  yard  of  felt),  -$1.15 

Two  chairs,  $  7.40  Pole,  $ 2.20 

With  hardwood  or  stained  floors  the  furnishing  and  care  of  a  house  are 
much  simplified.  If  one  must  have  carpets,  the  colors  should  be  neutral. 
The  best  quality  of  Canton  or  Japanese  matting  is  satisfactory  ;  it  is 
a  yard  wide  and  costs  fifty  cents  a  yard.  Next  to  matting,  the  most  sani- 
tary and  economical  carpet  is  good  body  Brussels.  It  wears  well,  and  the 
dust  does  not  get  under  it.  A  cheap,  loosely  woven  matting  or  woolen 
carpet  is  always  unsatisfactory. 

FLOOR  COVERINGS 

In  selecting  floor  coverings  there  are  several  important  considerations. 
The  design  and  quality  should  be  governed  by  the  treatment  the  rug  will 
necessarily  have. 

Hall 

A  hall  rug  or  carpet  will  receive  hard  wear ;  therefore,  the  quality 
should  be  good.  A  small  all-over  symmetrical  design  in  two  tones  of  one 
color  or  in  several  harmonizing  colors  will  show  dust  and  wear  less  than 
a  plain  surface  would  do. 

Rag  rug,  machine  made,  3  by  6  feet $2.18 

Hand-woven  rag  rug,  3  by  6  feet 7.50 

Scotch  wool  rug,  3  by  6  feet 4.00 

Hand-woven  wool  rug,  3  by  6  feet 6.00 

East  India  drugget,  3  by  6  feet 8.00 

Saxony,  3  by  6  feet 9.00 

Brussels  rug,  3  by  6  feet 9.00 

Oriental  rug,  3  by  6  feet 35.00 


COST    OF   FURNISHING   A   HOUSE  149 

Living  Room 

In  a  living  room  the  floor  covering  will  be  worn  all  over  equally. 
Since  there  is  always  a  variety  of  colors  and  forms  in  a  living  room,  it  is 
well  to  keep  the  floor  covering  as  plain  as  possible.  A  rug  with  a  plain 
center  and  a  darker  border  of  the  some  color  is  excellent  in  this  room, 
particularly  if  the  walls  or  hangings  are  figured.  If  they  are  plain, 
the  rug  or  carpet  may  have  a  small,  indefinite  figure.  If  several  domestic 
rugs  are  used  in  the  same  room,  they  should  be  exactly  alike  in  design  and 
color.  If  small  Oriental  rugs  are  used,  they  will,  of  course,  differ  in 
design,  but  they  should  be  as  nearly  as  possible  in  the  same  tone. 

Good  Living-room  Rugs 

Crex  or  grass  rug,  9  by  12  feet $  8. 50 

Rag  rugs,  9  by  12  feet 310.00  to  45.00 

Scotch  wool  rug,  9  by  12  feet $14.50  to  25.00 

Brussels,  9  by  12  feet 32.75 

Hand- woven  wool  rug,  9  by  12  feet 36.00 

East  India  drugget,  9  by  12  feet 43.00 

Saxony,  9  by  12  feet 50.00 

Oriental,  9  by  12  feet 200.00  up 

Dining  Room 

A  dining-room  rug  gets  very  hard  wear  in  spots.  It  should,  therefore, 
be  selected  in  as  good  quality  as  one  can  afford.  It  is  not  well  to  have  a 
perfectly  plain  rug  in  a  dining  room,  as  a  plain  surface  shows  crumbs  and 
spots  too  readily.  There  is  no  objection  to  having  a  dining-room  floor 
quite  bare,  if  the  floor  is  well  finished.  Inlaid  linoleum  also  makes  an 
excellent  floor  covering  for  a  dining  room  that  receives  very  hard  usage. 

The  best  coverings  for  this  room  are  : 

Crex  ingrain  rug,  9  by  12  feet       .......       $8.50 

Rag  rug,  9  by  12  feet $  10.00  to  45.00 

Brussels,  9  by  12  feet 32.75 

East  India  drugget,  9  by  12  feet 36.00 

Saxony,  9  by  12  feet 50.00 

Oriental,  9  by  12  feet 200.00  up 

Bedroom  and  Sewing  Room 

On  account  of  the  lint  which  accumulates  in  bedrooms,  it  is  a  good  plan 
to  keep  the  space  under  the  beds  bare,  so  that  it  may  be  dusted  every 
day.  Small  rugs  laid  where  most  needed  are  more  hygienic  in  sleeping 


150       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

rooms  than  are  large  rugs  and  carpets.  Plain  Chinese  matting  makes  a 
clean  floor  covering  when  the  boards  are  not  in  good  condition.  Although 
it  is  in  good  taste  to  use  a  carpet  or  one  large  rug  in  a  bedroom,  the 
preference  lies  among  the  following  : 

Small  rag  rugs,  3  by  6  feet $1.75 

Oval  braided  rag  rugs,  3  by  6  feet 2.50 

East  India  drugget,  3  by  6  feet 8.00 

Saxony,  3  by  6  feet 8.00 

Oriental,  3  by  6  feet 35.00 

EXAMPLES 

1.  A  family  has  an  income  of  $  1400.     They  buy  a  Brussels 
rug  3'  x  6'  for  $  9.     Are  they  extravagant? 

2.  How  much  cheaper  is  a  crex  rug,  9  by  12   feet,  than  a 
Brussels  the  same  size  ?     What  per  cent  cheaper  ? 

3.  A  dining-room  rug  is  purchased  for  $  49.75.     What  kind 
of  a  rug  is  it  ?     Is  it  suitable  for  a  family  with  an  income  of 
$  2500  ? 

4.  An  oval  braided  rag  rug  3'  x  6'  costs  $  2.50  and  will  last 
twice  as  long  as  a  small  rag  rug  that  costs  $  1.75  for  the  bed- 
room.    Which  is  more  economical  to  purchase?     How  much 
more  economical  is  it? 

The  Living  Room 

In  houses  or  apartments  of  but  five  or  six  rooms  there  is 
usually  but  one  living  room.  This  room  should  represent  the 
tastes  which  the  members  of  the  family  have  in  common.  The 
first  requisite  of  such  a  room  is  that  it  should  be  restful.  It 
is,  therefore,  advisable  to  use  a  wall  covering  that  is  plain  in 
effect.  Tan  is  good  in  a  room  that  is  inclined  to  be  dark ; 
gray-green  or  gray  itself  in  a  very  bright  living  room.  One 
large  rug  in  two  tones  of  one  color,  preferably  the  same  color 
as  the  walls,  is  better  than  a  figured  rug  for  this  room. 

Chairs  are  an  important  part  of  the  furnishing  of  a  living 
room.  It  is  well  to  have  comfortable  armchairs,  upholstered 


COST   OF   FURNISHING   A   HOUSE  151 

in  plain  material,  or  willow  chairs  with  cushions  of  chintz,  if 
this  material  is  used  as  curtains.  A  roomy  table  with  a  good 
reading  lamp  is  essential,  while  open  bookshelves,  a  writing 
desk  or  table,  a  sofa,  a  sewing  table,  and  a  piano  are  all  appro- 
priate furnishings  for  this  room. 


A  HARMONIOUSLY  FURNISHED  LIVING  ROOM 

The  curtains  may  be  of  figured  materials,  such  as  chintz  or 
cretonne.  Plain  scrim  or  net  curtains  may  be  used  over  cur- 
tains of  plain-colored  material  or  of  chintz  simply  to  give  the 
necessary  warmth  and  color  to  the  sides  of  the  room.  Valances 
are  used  to  reduce  the  apparent  height  of  a  window  and  to  give 
a  low  cozy  look  to  the  room.  Plants  are  always  appropriate  to 
use  in  sunny  windows,  and  pictures  of  common  interest,  framed 
in  polished  wood  or  dull  gilt  frames,  help  to  make  the  living 
room  attractive.  Use  very  little  bric-a-brac.  Nothing  which 
does  not  actually  contribute  to  the  beauty  of  the  room  should 
be  allowed  to  find  a  place  there. 


152       VOCATIONAL   MATHEMATICS   FOR   GIRLS 
PRICE  LIST  OF  LIVING-KOOM  FURNITURE 


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Table     .... 

$4.50 

$15.00 

$17.00 

$50.00 

$35.00 

$59.00 

$12.00 

Chair     .... 
Sofa       .     . 

17.00 

22.50 

25.00 

45.00 
55.00 

30.50 
68.00 

50.00 
100.00 

12.75 
23.50 

Armchair   .     .     . 

20.00 

38.00 

32.00 

65.00 

9.75 

Desk  chair      .     . 

2.75 

6.75 

7.75 

15.00 

4.75 

15.00 

8.25 

Desk      .... 

9.75 

19.50 

21.75 

90.00 

28.00 

90.00 

37.50 

Bookcase   . 

9.00 

9.00 

11.25 

100.00 

25.00 

100.00 

13.50 

Sewing  table  .     . 

5.00 

5.00 

6.00 

17.00 

18.50 

13.50 

Tea  table    .     .     . 

1.50 

1.50 

2.00 

35.00 

12.00 

7.25 

Footstool    .     .     . 

2.25 

3.75 

3.00 

6.00 

4.50 

6.00 

5.25 

Wood  box  or  rack 

5.00 

5.00 

5.00 

5.00 

3.50 

Magazine  stand  . 

6.00 

6.75 

8.25 

10.00 

8.50 

8.50 

12.75 

Piano     .... 

200.00 

250.00 

450.00 

450.00 

Music  cabinet 

6.75 

6.75 

8.25 

28.00 

10.00 

c.          /Gas,    $5.00 
Stoves{  Coal,  17.00 


Wood      .     .    $15.00 
Wood  or  coal    25.50 


Franklin  grate  or  andirons, 
wood  or  coal  $35.00 


EXAMPLES 

1.  How  much  more  will  it  cost  to  furnish  a  living  room  with 
library  furniture  than  with  willow  furniture  ? 

2.  How  much  more  will  it  cost  to  furnish  a  living  room  with 
hand-made  oak  furniture  than  with  colonial  designs  in  oak  ? 

3.  A  living  room  was  furnished  with  the  following  furni- 
ture.    Ascertain  from  the  price  list  what  kind  of  furniture  it  is. 

Large  round  table    and   small         Curtains     and    shades    for    three 


table,  $7.95 

Six  chairs  and  couch,  $  51.15 
Bookcase  or  shelves,  $  9.85 

What  is  the  cost  ? 


windows,  $6.15 
Rug  and  draperies,  $34.15 
Incidentals,  $  24.65 


COST    OF   FURNISHING   A   HOUSE  153 

The  Bedroom 

When  one  stops  to  think  that  about  one-third  of  one's  life  is 
spent  in  sleep,  it  is  easy  to  understand  that  the  first  requisite 
in  the  furnishing  of  the  bedroom  is  that  it  be  fresh  and  clean. 


A  COMFORTABLE  BEDROOM 

Unless  the  room  must  be  used  as  a  study  or  sitting  room  in 
the  daytime,  the  amount  of  furniture  should  be  reduced  as 
much  as  possible.  The  necessary  pieces  are  a  bed,  a  dressing 
case  which  should  be  generous  in  drawers  and  mirror,  a  wash- 
stand,  a  toilet  set,  towel-rack,  one  easychair  and  one  plain  one, 
a  small  table,  a  rug,  and  window  shades.  If  space  and  money 
permit,  a  couch  is  desirable.  Naturally,  a  writing  desk,  book- 
shelves, and  pictures  all  add  to  the  attractiveness  of  such  a 
room.  If  one  cannot  have  bare  floors,  the  next  best  thing  is 
good  matting.  A  woolen  carpet  is  not  desirable  for  a  sleeping 
room.  All  draperies  should  be  of  materials  that  will  hold 
neither  dust  nor  odor. 


154       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

The  bed  is  the  most  important  article  in  the  room.  The 
springs  and  mattress  should  be  firm  enough  to  support  all  parts 
of  the  body  when  it  is  in  a  horizontal  position. 

The  walls  should  be  light  in.  color  and  the  woodwork  white 
if  possible.  The  furniture  also  may  be  white,  although  dull- 
finished  mahogany  in  colonial  designs,  with  small  rugs  on 
the  floor,  makes  a  charming  bedroom.  One  set  of  draw  cur- 
tains, of  figured  chintz  if  the  walls  are  plain,  and  of  plain-colored 
material  if  the  walls  have  a  small  figure,  is  enough  for  each 
window. 

The  furnishings  of  a  young  girl's  bedroom  should  be  carried 
out  in  her  favorite  color,  and  to  the  usual  bedroom  furniture 
should  be  added  a  desk,  lamp,  worktable,  and  bookshelves. 

The  bedroom  for  a  growing  boy  should  be  his  own  sitting 
room  and  study  as  well ;  a  place  where  he  can  entertain  his 
friends,  do  his  studying,  and  develop  his  hobbies.  The  walls, 
hangings,  couch  cover,  etc.,  should  be  very  plain,  as  a  boy 
usually  has  a  collection  of  trophies  which  need'  the  plainest 
sort  of  a  background  in  order  to  prevent  the  room  from  looking 
cluttered.  Instead  of  the  usual  bed  he  should  have  an  iron- 
framed  couch,  which  in  the  daytime  may  be  made  up  with  a 
plain  dark  cover  with  cushions,  to  be  used  as  a  couch.  A  chif- 
fonier, an  armchair,  bookshelves,  writing  table,  and  one  or  two 
small  rugs  will  complete  the  furnishings  of  the  boy's  bedroom. 

EXAMPLES 

1.  Sheets  should  be   of   ample  length  and  breadth.     The 
finished  sheets  should  be  nearly  three  yards  long.     How  many 
inches  long  ? 

2.  The  supply  of  bedroom  linen,  blankets,  and  counterpanes 
for  a  small  house  is  as  follows : 

12  sheets  @  §0.85  4  pairs  blankets  @  $8.00 

12  pillow  cases  @  $  .40  2  counterpanes  @  $  2.50 

24  towels  @$  0.50 

What  is  the  total  cost  ? 


COST    OF   FURNISHING   A   HOUSE 
PRICE  LIST  OF  BEDROOM  FURNITURE 


155 


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Bed    .... 

$9.75 

$16.50 

$18.75 

$21.00 

$55.00 

$30.00 

$56.00 

Mattress      .     . 

3.35 

16.00 

16.00 

16.00 

36.00 

36.00 

36.00 

to 

to 

to 

to 

16.00 

25.00 

25.  CO 

25.00 

Box  spring  .     . 

20.00 

20.00 

20.00 

20.00 

20.00 

20.00 

20.00 

Crib  (iron)  .     . 

12.75 

12.75 

12.75 

12.75 

12.75 

12.75 

Crib  mattress  . 

3.75 

9.00 

9.00 

9.00 

9.00 

9.00 

Pillows  (pair)  . 

1.25 

2.10 

2.10 

2.10 

6.00 

5.25 

5.25 

Bureau   .     .     . 

9.75 

22.50 

25.00 

27.50 

75.00 

50.00 

67.50 

Washstand 

1.50 

2.00 

2.75 

3.50 

6.00 

10.00 

(enamel 

iron) 

Dressing  table 

9.00 

12.57 

14.25 

15.75 

55.00 

26.00 

48.00 

Chiffonier    (no 

9.00 

12.00 

14.25 

16.'50 

100.00 

39.00 

60.00 

mirror)     .     . 

(high- 

boy) 

Chair      .     .     . 

2.75 

4.50 

5.25 

6.00 

10.00 

6.50 

8.00 

Rocking  chair  . 

2.75 

6.75 

7.75 

8.75 

9.00 

6.50 

8.25 

Waist  box   .     . 

Home- 

made 

2.50 

3.50 

4.50 

20.00 

16.00 

4.50 

Desk  .... 

4.50 

9.75 

10.75 

11.75 

60.00 

20.00 

28.50 

Armchair    . 

6.75 

7.75 

8.75 

24.00 

8.00 

7.50 

Couch     .     .     . 

5.00 

13.25 

60.00 

50.00 

25.00 

(iron 

frame) 

(box) 

Bookshelves 

Home- 

made 

9.00 

10.50 

12.00 

(built  in) 

21.50 

13.50 

Cheval  glass     . 

11.25 

15.50 

16.50 

18.00 

50.00 

25.00 

ctovpsfGas,    $5.00      Wood.     .     .$15.50      Franklin  grate  or  andirons, 
a  \Coal,  17.00      Wood  or  coal     25.50         wood  or  coal     .     $35.00 

156       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

3.  If  a  person  spends  one-third  of  a  life  in  a  bedroom,  how 
many  hours  a  day  are  spent  in  the  bedroom  ? 

4.  A  bedroom  is  furnished  with  the  following  furniture : 

Enameled  bedstead  withsprings,  Dimity  for  draping  bed,  washstand 

$7.50  and  two  windows,    twenty-one 

A  dressing  case,  $  15.00  yards,  $  3.15 

A  plain    wooden    table    to   be  Enameled  cloth  for  washstand,  $.55 

used  as  washstand,  $  1.00  Two  pillows,  $4.00 

A  small  table  $  2.00  Toilet  set,  $  3.00 

•  Chair,  $  2.00  Shades  for  two  windows,  1 1.00 

Mattress,  $  5.00  Towel  rack,  $  .75 
Rug,  $3.00 

What  is  the  total  cost  ? 

5.  What  will  it  cost  to  furnish  a  bedroom  with  simple  cot- 
tage furniture  as  provided  above  ? 

6.  What  will  it  cost  to  furnish  a  bedroom  with  the  good 
grade  of  oak  furniture  in  gloss  enamel  ?     What  is  the  least 
income  a  family  should  have  in  order  to  buy  this  furniture  ? 

7.  What  will  it  cost  to  furnish  a  bedroom  with  real  mahog- 
any furniture  ?     What  is  the  least  income  one  should  have  in 
order  to  buy  this  furniture  ? 

The  Dining  Room 

The  dining  room  does  not  require  a  great  deal  of  furniture, 
but  what  there  is  should  be  of  the  most  substantial  kind. 
Mahogany  and  oak  are  the  woods  to  be  preferred.  The  table 
should  be  broad,  stand  well,  with  the  legs  so  placed  that  they 
will  not  interfere  with  the  comfort  of  any  one  seated  at  the 
table.  The  chairs  should  be  well  made,  with  broad,  deep 
seats  and  high,  straight  backs.  Unless  one  can  afford  the 
right  kind  of  a  sideboard  it  is  better  to  purchase  a  sideboard 
table  in  simple  design.  A  piece  of  Japanese  matting  in  the 
center  of  the  dining  room  floor  is  quite  satisfactory  when  the 
floor  is  stained. 


COST   OF   FURNISHING   A    HOUSE 


157 


The  room  in  which  the  family  assembles  several  times  each 
day  to  enjoy  its  meals  together  should  be  the  most  cheerful 
room  in  the  house. 


AN  ATTRACTIVE  DINING  ROOM 

Because  there  is  so  much  attractive  blue-and-white  china  in  use, 
many  persons  want  dining  rooms  with  blue  walls.  This  is  usually  a  mis- 
take, as  blue  used  in  large  quantities  absorbs  the  light  and  makes  a  room 
gloomy,  particularly  on  dark  days  and  at  night.  By  using  colonial  yel- 
low on  the  walls,  with  hangings,  rug,  and  decorative  china  in  blue  and 
white,  one  has  an  almost  ideal  arrangement.  There  are  many  charming 
landscape  and  foliage  papers  on  the  market  which,  used  without  pictures 
against  them,  but  with  bulbs  or  plants  blooming  on  the  windowsills  and 
with  hangings  of  plain,  semitransparent,  colored  material  make  most 
delightful  rooms. 

Plate  rails  or  racks  reduce  the  apparent  height  of  an  over-high  ceiling. 
It  is  better  to  use  a  simple  flat  molding  than  to  crowd  a  plate  rail  full  of 
inharmonious  objects. 

Ugly  glass  domes  on  lamps  are  being  replaced  by  silk  ones  with  deep 
silk  fringe  or,  better  still,  the  center  light  is  abandoned  in  favor  of  side 
wall  fixtures  in  all  of  the  rooms.  Candles,  prettily  shaded,  are  used  on 
the  table  at  night,  with  a  jar  of  flowers  or  fruit  as  a  centerpiece. 


158       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


EXAMPLES 

1.  What  will  the   following  cottage   dining-room  furniture 
cost  ?     (Include  the  items  given  in  the  price  list  below.) 

2.  What  will  the  following  oak  dining-room  furniture  cost  ? 

3.  What  will  the  following  real  mahogany  dining-room  fur- 
niture cost  ? 

PRICE  LIST  OF  DINING-ROOM  FURNITURE 


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Table     .... 

$0.00 

$30.00 

$10.50 

$12.00 

$85.00 

$21.00 

$16.00 

Chair     .... 

2.75 

4.50 

5.50 

6.50 

10.00 

6.50 

8.25 

Armchair  . 

2.75 

6.75 

7.75 

8.75 

15.00 

10.00 

Serving  table  .     . 

8.25 

9.00 

10.50 

12.75 

35.00 

18.00 

28.00 

Buffet    .... 

18.00 

27.50 

21.00 

24.00 

125.00 

34.00 

82.50 

China  closet    . 

15.00 

30.00 

34.50 

39.00 

60.00 

45.00 

Serving  table  on 

wheels    .     .     . 

16.75 

16.75 

30.50 

34.00 

27.00 

27.00 

24.00 

Screen   .... 

3.75 

5.00 

4.50 

5.25 

25.00 

20.00 

High  chair 

2.50 

2.50 

4.15 

5.50 

10.00 

9.00 

8.00 

Stoves  /  Gas'    ^5-°°      Wood  •     •     •  $15.50    Franklin  grate  or  andirons, 
\Coal,  17.00      Wood  or  coal    25.00        wood  or  coal .     .     $35.00 

4.   What  will  it  cost  to  furnish  a  home  on  a  moderate  scale 
with  china  of  the  following  amounts  and  kinds  : 

I  dozen  soup  plates  (to  be  used  for  cereals  also)  .     .  $2.35 

\  dozen  dinner  plates 2.25 

1  dozen  lunch  plates  (used  also  for  breakfast  and  for 

salads) 3.85 

\  dozen  dessert  plates 1.60 


COST   OF   FURNISHING   A   HOUSE  159 

£  dozen  bread-and-butter  plates §  0. 70 

\  dozen  coffee  cups  and  saucers 3.30 

^  dozen  tea  cups  and  saucers 2.80 

\  dozen  after-dinner  coffee  cups  and  saucers    .     .     .  2.35 

1  teapot 1.90 

1  coffee  pot 2.00 

1  covered  hot-milk  jug  or  chocolate  pot 2.60 

1  large  cream  pitcher .70 

1  small  platter  or  chop  platter 2.50 

3  odd  plates  for  cheese,  butter,  etc .95 

Covered  dish 2.80 

\  dozen  egg  cups 1.50 

5.  What  will  it  cost  to  furnish,  a  home  on  a  moderate  scale 
with  glass,    colonial   period,   of   the   following   amounts   and 
kinds : 

\  dozen  tumblers -$0.50 

\  dozen  sherbet  glasses .35 

\  dozen  dessert  plates 1.25 

\  dozen  ringer  bowls .75 

Sugar  bowl  and  cream  pitcher .50 

Dish  for  lemons 50 

Dish  for  nuts        .25 

Pitcher 50 

Candlesticks .65 

Vinegar  and  oil  cruets .50 

Berry  dish 25 

I  dozen  iced-tea  glasses .75 

\  dozen  individual  salt  cellars .60 

6.  What  will  it  cost  to  furnish  a  home  on  a  moderate  scale 
with   silver,  pilgrim    pattern,  of   the  following  amounts    and 
kinds : 

1  dozen  teaspoons $14.00 

\  dozen  dessert  spoons  (used  for  soup  also)    .     .     .  9.50 

4  tablespoons 9.50 

1  dozen  dessert  forks  (used  also  for  breakfast,  lunch, 

salad,  pie,  fruit,  etc.) 19.00 

\  dozen  dessert  knives 11.00 


160       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

\  dozen  table  knives  with  steel  blades  and  ivoroid 

handles        $2.00 

Carving  set  to  match  steel  knives 4.00 

\  dozen  table  forks 12.00 

2  fancy  spoons  for  jellies,  bonbons,  etc.  ($  1.50  each)  3.00 

2  fancy  forks  for  olives,  lemons,  etc.  ($1.50  each)  .  3.00 

\  dozen  after-dinner  coffee  spoons 5.00 

\  dozen  bouillon  spoons 8.00 

\  dozen  butter  spreaders 1.50 

1  gravy  ladle 4.75 

Saltspoon -  ....  .20 

Sugar  tongs 2.25 

7.  What  will  it  cost  to  furnish,  a  home  on  a  moderate  scale 
with  silver-plated  ware  of  the  following  amounts  and  kinds : 

Covered  vegetable  dish    (cover  may  be   used  as  a 

dish  by  removing  handle) $10.00 

Platter 11.50 

Pitcher 12.00 

Coffee  pot 12.50 

Toast  rack 4.50 

Small  tray 6.50 

Sandwich  plate       6.00 

Silver  bowl 9.00 

Egg  steamer 8.00 

Bread  or  fruit  tray 5.50 

Tea  strainer       1.00 

Candlesticks,  each 3.75 

Household  Linen 

The  quality  of  linen  in  every  household  should  be  the  best  that  one 
can  possibly  afford.  The  breakfast  runners  and  napkins  are  to  be  made 
by  hand,  of  unbleached  linen  such  as  one  buys  for  dish  towels.  With 
insets  of  imitation  filet  lace  these  are  very  attractive,  durable,  and  easy 
to  launder. 

1.  What  is  the  cost  of  supplying  the  following  amount  of 
table  and  bed  linen  for  a  couple  with  an  average  income  of 
%  1400,  who  are  about  to  begin  housekeeping  ? 


COST    OF   FURNISHING   A   HOUSE  161 

Table  Linen 

2  dozen  22-inch  napkins,  at  $3.00  a  dozen. 

2  dozen  12-inch  luncheon  napkins,  at  $4.50  a  dozen. 

(Luncheon  napkins  at  $1.00  a  dozen  if  made  by  hand  of  coarse  linen.) 
2  two-yard  square  tablecloths,  at  $1.25  a  yard. 
Two-yard  square  asbestos  or  cotton  flannel  pad  for  table,  at  $  1.00. 
\  dozen  square  tea  cloths,  $12.00. 
^  dozen  table  runners  for  breakfast,  at  $2.40. 
1  dozen  white  fringed  napkins,  at  $1.20. 
4  tray  covers,  at  65  cts. 
1  dozen  finger-bowl  doilies,  at  $3.00. 
1  dozen  plate  doilies,  at  $  3.00. 

Bed  Linen 

4  sheets  (extra  long)  for  each  bed,  at  $  1.10. 
4  pillow  cases  for  each  pillow,  at  20  cts. 

1  mattress   protector  for  each  bed,  with   one  extra  one   in  the   house, 

at  $1.50. 

2  spreads  for  each  bed,  at  $  2.50. 

1  down  or  lamb's-wool  comforter  for  each  bed,  at  $  6. 

1  pair  of  blankets  for  each  bed,  with  2  extra  pairs  in  the  house,  at  $  8. 

£  dozen  plain  huckaback  towels  for  each  person,  at  25  cts. 

3  bath  towels  for  each  person,  at  30  cts. 

£  dozen  washcloths  for  each  person,  at  11  cts. 

1  bath  mat  in  the  bathroom,  2  in  reserve,  at  $1.50. 

• 

The  Sewing  Room 

Even  in  a  small  house  there  is  sometimes  an  extra  room  which  may  be 
fitted  up  as  a  sewing  room  in  such  a  way  as  to  be  very  convenient  and 
practical,  and  at  the  same  time  so  attractive  as  to  serve  occasionally  as  an 
extra  bedroom.  This  room  should  be  kept  as  light  as  possible  and  should 
be  so  furnished  that  it  may  easily  be  kept  clean. 

EXAMPLE 

1.  What  will  it  cost  to  furnish  a  sewing  room  with  the  fol- 
lowing articles  ? 

Sewing  machine  with  flat  top  to  be  Used  as  a  dressing  table    .     .  $  20.00 

Chair 1.25 

Box  couch ....  13.25 

Chiffonier .  9.00 


162       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

Mirror  against  a  door $11.25 

Low  rocking-chair  without  arms 1.50 

Cutting  table,  box  underneath  ;  tilt  top  to  be  used 6.75 

Clothes  tree 3.38 

The  Kitchen 

The  room  in  which  the  average  housekeeper  spends  the 
greater  part  of  her  time  is  usually  the  least  attractive  room 
in  the  house,  whereas  it  should  be  made  —  and  we  learn  by 
visiting  foreign  kitchens  that  it  may  be  made  —  a  picturesque 
setting  for  one  of  the  finest  arts  —  the  art  of  cookery. 


A  CONVENIENT  KITCHEN 

The  woodwork  should  be  light  in  color,  the  walls  should  be  painted 
with  oil  paint,  or  covered  with  washable  material,  this  also  in  a  light 
color.  A  limited  number  of  well-made,  carefully  selected  utensils  will 
be  found  more  useful  than  a  large  supply  purchased  without  due  con- 
sideration as  to  their  real  value  and  the  need  of  them.  Of  course,  the 
style  of  living  and  the  size  of  the  family  must  to  some  extent  control  the 
number,  size,  and  kind  of  utensils  that  are  required  in  each  kitchen.  As 
in  all  the  other  furnishings,  the  beginner  will  do  well  to  purchase  only 
the  essential  articles  until  time  demonstrates  the  need  of  others. 


COST    OF    FURNISHING   A   HOUSE 


163 


EXAMPLES 


•>  i 


1.  What  will  it  cost  to  furnish  your  kitchen  V 

Stoves  — Gas 12.50,  $  10.00,  $30.00 

Blue-flame  kerosene 10.25 

Coal,  wood,  gas 86.00 

Coal  and  wood 49.75 

Small  electric 33.00 

Table    .     .     .  $2.10;  .-$9.00  (drop  leaf)  ;$  11.25  (white  enamel  on  steel) 

Chair $1.87,  $6.75 

Ice  chest $7.00,  $  15.00,  $40.00  (white  enamel) 

Kitchen  cabinet $28.00,  $29.00  (white  enamel  on  steel) 

Linoleum       .     .     .    60c.  square  yard,  printed;  $  1.60  square  yard,  inlaid 

2.  What  will  the  following  small  kitchen  furnishings  cost  ? 


Small-sized  ironing  board  .  $0.35 
Small  glass  washboard  .  .  .35 
Clothesline  and  pins  ...  .59 
2  irons,  holder  and  stand  .  .70 
2-gallon  kerosene  can  .  .  .45 
Small  bread  board  ...  .15 
Hack  for  dish  towels  ...  .10 

6  large  canisters 60 

Wooden  salt  box 10 

1  iron  skillet 30 

1  double  boiler 1.00 

Dish  drainer 25 

2  dish  mops 10 

Wire  bottle  washer     .     .     .        .10 

•  Small  rolling  pin 10 

Chopping  machine  ...  1.10 
Large  saucepan 30 

3  graduated   copper,  enam- 
eled   or    nickel    handled 
dishes 50 

2    covered    earthenware    or 

enameled  casseroles  .  .  1.50 
2  pie  plates  enameled  .  .  .20 
Alarm  clock  1.00 


Small  covered  garbage  pail .        .35 

Scrubbing  brush 20 

Broom  and  brushes     .     .     .        .60 

1  quart  ice-cream  freezer     .      1.75 

Roller  for  towel 10 

Bread  box 50 

4  small  canisters 40 

2  sheet-iron  pans  to  use  as 
roasting  pans 20 

Dishpan  (fiber)      ,     .     .     .        .50 

Plate  scraper 15 

Soap  shaker 10 

Vegetable  brush 05 

Muffin  tins 25 

Granite  soup  kettle     .     .     .        .45 

3  graduated  small  saucepans        .30 

Glass  butter  jar 35 

6  popover  or  custard  cups    .        .30 

Soap  dish 25 

Knives,    forks,    egg   beater, 

lemon  squeezer,  etc.  .  .  5.50 
Sink  strainer,  brush,  and 

shovel 50 

Galvanized-iron  scrub  pail  .  .30 


1  Consider  income  of  family  aud  size  of  kitchen. 


164       VOCATIONAL   MATHEMATICS   FOR   GIRLS 


EXAMPLES   IN   LAYING  OUT   FURNITURE 

Considerable  practice  should  be  giveu  in  laying  out  furniture  according 
to  scale. 

1.  A  bedroom  12'  x  10'  6"  faces  the  south,  and  has  2  win- 
dows, 3'  6"  wide,  1  window,  3'  6",  two  feet  from  corner  of  west 
sidej  and  a  door  3'  wide  two  feet  from  east  wall.  This  room 
is  to  contain  the  following  furniture : 


1  bed,  6'  6"  x  4' 
1  dresser,  3'  x  1'6" 


E 


& 

SOLUTION 

1  dining  table,  5'  in  diameter 
1  buffet,  4'  x  2' 


1  table,  2'  6"  x  3' 

2  chairs,  1'  6"  x  2' 

Draw  a  plan  showing  the 
most  artistic  arrangement  of 
furniture.  Scale  -J-"  =  V. 

2.  A  dining  room  15'  x  18' 
faces  the  east,  and  has  two 
windows  3'  6"  wide  on  the 
east  side,  2  windows  3'  6"  on 
the  north  side,  folding  doors  6 
wide  in  the  center,  on  the 
south  side.  Draw  a  plan  and 
place  the  following  furniture  in 
it  in  the  most  artistic  manner : 

6  chairs,  2'  x  1'  6" 
Scale,  \"  =  I' 


3.  A  living  room  15'  x  18'  faces  the  north  and  has  2  win- 
dows 3'  6"  wide  on  the  north  side,  2  windows  3'  6"  on  the 
west  side,  and  folding  doors  on  the  south  side.  Draw  a  plan 
and  place  the  following  furniture  in  the  most  artistic  manner : 


1  settee 
1  table 
1  desk  and  chair 


2  easy-chairs 
2  rockers 
Scale  i"  =  I' 


4.    A  kitchen  12'  x  10'  6"  faces  the  south  and  has  2  windows 
3'  6"  wide  on  the  south   side,   1   on  the  west  side,   two  feet 


COST   OF   FURNISHING  A   HOUSE  165 

from  the  north  comer,  a  door  3'  wide,  two  feet  from  the  north- 
east corner  that  leads  into  the  dining  room.  Draw  a  plan  and 
place  the  furniture  in  proper  places : 

1  kitchen  range  1  table 

.      1  sink  2  chairs 

•   2  set  tubs  Scale  \"  =  V 

REVIEW  EXAMPLES 

1.  A  living  room  was  fitted  out  with  the  furniture  in  the  list 
below.     What  kind  of  furniture  is  it  ?     What  is  the  cost  ? 

Large    round    table    and   small  Curtains  and  shades  for  three 

table,  $8.00  windows,  §  6.30 

Six  chairs  and  couch,  $  50.00  Rug  and  draperies,  $  34.00 

Bookcase  or  shelves,  $  10.00  Incidentals,  $25.00 

2.  A  hall  was  furnished  with  the  following  articles.     What 
was  the  total  cost  ?     What  kind  of  furniture  was  used  ? 

Seat,  $12.00  Rug,  $10.00 

Mirror,  $2.00  Umbrella  stand,  $2.00 

Table,  $  2.00  Table  cover,  $  1.00 

Two  chairs,  $7.50  Pole,  $3.00 

3.  A  family  of  seven  —  three  grown  people  and  four  chil- 
dren —  lived  in  a  southern  city  on  $  600  a  year.     The  monthly 
expense  was  as  follows  : 

House  rent,  $  12.00  Bread,  $  3.50 

Groceries,  $  12.00  Beef,  $3.50 

Washing,  $  5.00  Vegetables,  $3.00 

What  is  the  balance  from  the  monthly  income  of  $  50  for 
clothing  and  fuel  ? 

4.  What  is  the  cost  of  the  following  kitchen  furniture  ? 

1  kitchen  chair,  $  1.25  1  broom,  50  cents 

1  table,  $  1.50  Kitchen  utensils,  $  8.50 


166       VOCATIONAL   MATHEMATICS   FOR   GIRLS 


5.    What  is  the  cost  of  the  following  living-room  furniture  ? 
How  much  income  should  a  family  receive  to  buy  this  furniture  ? 


Overstuffed  chair,  $12.50 
2  willow  chairs,  $  6  each 
1  willow  stool,  $4.25 
1  rag  rug,  $  9.50 
1  newspaper  basket,  $2.25 
12  yards  of  cretonne,  35  cents  a 
yard 


1  green  pottery  lamp  bowl,  $  3.00 
1  wire  shade  frame,  50  cents 
7  yards  of  linen,  at  50  cents  a  yd. 
10    yards   of    cotton   fringe,    at   5 

cents  a  yd. 

6  yards  of  net,  at  25  cents  a  yd. 
Table,  48  by  30  inches,  $  7.00 


6.    What  is  the  cost  of  the  following   bedroom  furniture? 
How  much  income  should  a  family  have  to  buy  this  furniture  ? 


1  bed  pillow,  $1.00 

10  yards  of  white  Swiss,  at  25  cents 

a  yd. 
8  yards  of  pink  linen,  at  50  cents 

a  yd. 

1  comfortable,  $4.25 
Sheets  and  blankets  for  one  bed, 

$6.00 
3  yards  of  cretonne,  at  35  cents  a  yd. 

7.  What  is  the  cost  of  the  following  bedroom  furniture  ? 
How  much  income  should  a  family  have  to  warrant  buying 
this  furniture  ? 


1  bed  spring,  $3.50 

1  single  cotton  mattress,  $4.25 

1  chiffonier,  $6.50 

1  dressing  table,  $2.25 

1  mirror,  $2.75 

1  armchair,  $4.00 

1  rag  rug,  $3.25 

2  pillows,  75  cents  each 


2  white  iron  beds,  at  $4.25  each 
2  single  springs,  at  $2.50  each 
2  cotton  mattresses,   at  $4.25 

each. 

2  bed  pillows,  at  $  1.00  each 
1  dressing  table,  $  5.50 
1  white  desk,  $6.75 
1  chiffonier,  $6.50 
1  dressing-table  mirror,  $3.25 
1  chiffonier  mirror,  $1.50 
1  rag  rug,  $3.25 

I  wastepaper  basket,  .50 

II  yards  of  cretonne,  at  35  cents 
a  yd. 


5  yards  of  yellow  sateen,    at  25 

cents  a  yd. 

2  comfortables,  at  $  4.25  each 
10  yards  of   cream   sateen,   at  25 

cents  a  yd. 
15  yards  of  cotton  fringe,  at  5  cents 

a  yd. 

1  willow  chair,  $  6.00 
1  cushion,  75  cents 
4  yards  of  net,  at  25  cents  a  yd. 
Sheets  and  blankets  for  two  beds, 

$  12.00 
1  dressing  table  chair,  $4.50 


HEAT  AND   LIGHT  167 

8.   What  is  the  cost  of  the  following  dining-room  furniture  ? 
What  income  should  one  receive  to  buy  this  furniture  ? 

6  dining-room  chairs,  $4.50  lOyardsof  cretonne,  at  35  cents  a  yd. 

1  dining  table,  $6.75  One  wire  shade  frame,  50  cents 

1  serving  table,  $  6.25  Table  linen,  $  8.00 

1  rag  rug,  $9.50  Silverware,  $7.50 

1  set  of  dishes,  $  9.75  1  willow  tray,  $3.25 


HEAT  AND  LIGHT 

Value  of  Coal  to  Produce  Heat 

Several  different  kinds  of  coal  are  used  for  fuel.  Some  grades  of  the 
same  coal  give  off  more  heat  in  burning  than  others.  The  heating  value 
of  a  coal  may  be  determined  in  three  ways  :  (1)  by  chemical  analysis  to 
determine  the  amount  of  carbon  ;  (2)  by  burning  a  definite  amount  in  a 
calorimeter  (a  vessel  immersed  in  water)  and  noting  the  rise  in  tempera- 
ture of  the  water  ;  (3)  by  actual  trial  in  a  stove  or  under  a  steam  boiler. 
The  first  two  methods  give  a  theoretical  value  ;  the  third  gives  the  real 
result  under  the  actual  conditions  of  draft,  heating  surface,  combustion, 
etc. 

The  coal  generally  used  for  household  purposes  in  the  Eastern  states 
comes  from  the  anthracite  fields  of  Pennsylvania.  This  coal,  as  shipped 
from  the  mines,  is  divided  into  several  different  grades  according  to  size. 
The  standard  screening  sizes  of  one  of  the  leading  coal-mining  districts  are 
as  follows  : 

Broken,  through  4|"  round  Pea,  through  f"  square 

Egg,  through  2f"  square  Buckwheat,  through  ±"  square 

Stove,  through  2"  square  Rice,  through  f  "  round 

Nut,  through  1|"  square  Barley,  through  \"  round 

The  last  three  sizes  given  above  are  too  small  for  household  use  and 
are  usually  purchased  for  generating  steam  in  large  power-plant  boilers. 

Coke  is  used  to  some  extent  in  localities  where  it  can  be  obtained  at  a 
reasonable  price  in  sizes  suitable  for  domestic  purposes.  The  grades  of 
coke  generally  used  for  this  purpose  are  known  as  nut  and  pea.  The  use 
of  coke  in  the  household  has  one  principal  objection.  It  burns  up  quickly 
and  the  fires,  therefore,  require  more  attention.  This  is  due  to  the  fact 
that  a  given  volume  of  coke  weighs  less  and  therefore  contains  less  heat 
than  other  fuel  occupying  the  same  space  in  the  stove  or  furnace. 


168       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

The  chief  qualities  which  determine  the  value  of  domestic  coal  are  its 
percentage  of  ash  and  its  behavior  when  burned.  Coal  may  contain  an 
excessive  amount  of  impurities  such  as  stone  and  slate,  which  may  be  easily 
observed  by  inspection  of  the  supply.  The  quality  of  domestic  coke 
depends  entirely  upon  the  grade  of  coal  from  which  it  has  been  made, 
and  may  vary  as  much  as  100  °fo  in  the  amount  of  impurities  contained. 

Aside  from  the  chemical  characteristics  of  domestic  coal,  the  most  im- 
portant factor  to  consider  in  selecting  fuel  for  a  given  purpose  is  the  size 
which  will  best  suit  the  range  or  heater.  This  depends  on  the  amount 
of  grate  surface,  the  size  of  the  fire-box,  and  the  amount  of  draft. 

EXAMPLES 

1.  Hard  coal  of  good  quality  has  at  least  90  %  of  carbon. 
How  much  carbon  in  9  tons  of  hard  coal  ? 

2.  A  common  coal  hod  holds  30  pounds  of  coal.     How  many 
hods  in  a  ton  ? 

3.  If  coal  sells  for  $  8.25  in  June  and  for  $  9.00  in  January, 
what  per  cent  is  gained  by  buying  it  in  June  rather  than  in 
January  ?     When  is  the  most  economical  time  to  buy  coal  ? 

4.  The  housewife  buys  kerosene  by  the  gallon.     If  the  price 
per  gallon  is  13  cts.  and  live  gallons  cost  55  cts.,  what  is  the  per 
cent  gained  by  buying  in  5-gallon  can  lots  ? 

5.  If  kerosene  sells  for  $4.60  a  barrel,  what  is  the  price  per 
gallon  by  the  barrel  ?     What  per  cent  is  gained  over  single 
gallons  at  13  cts.  retail  ?     What  is  the  most  economical  way 
to  buy  kerosene  ?     (A  barrel  contains  42  gallons.) 

How  to  Read  a  Gas  Meter 1 

1.  Each  division  on  the  right-hand  circle  denotes  100  feet ; 
on  the  center  circle  1000  feet ;  and  on  the  left-hand  circle 

10,000  feet.  Read  from  left- 
hand  dial  to  right,  always  tak- 
ing the  figures  which  the  hands 
have  passed,  viz.  :  The  above 
dials  register  3,  4,  6,  adding 
1  Gas  is  measured  in  cubic  feet. 


HEAT  AND   LIGHT 


169 


two  ciphers  for  the  hundreds,  making  34,600  feet  registered. 
To  ascertain  the  amount  of  gas  used  in  a  given  time,  deduct 
the  previous  register  from  the  present,  viz. : 

Register  by  above  dials 34,600 

Register  by  previous  statement 18,200 

Given  number  of  feet  registered 16,400 

16,400  feet  @  90  cts.  per  1000  costs  what  amount  ? 

2.  If  a  gas  meter  at  the  pre- 
vious reading  registered  82,700    ^  ^    ^^          ^ 
feet,  and  to-day  the  dials  read 

as  follows, 

what  is  the  cost  of  the  gas  at  95  cts.  per  1000? 

3.  What  is  the  cost  of  the  gas  used  during  the  month  from 
the  reading  on  this  meter,  if 

the  previous  reading  was  6100 
feet  ?  The  rate  is  $  1.00  per 
1000  cu.  ft.  less  ten  per  cent, 
if  paid  before  the  12th  of  the 
month.  Give  two  answers. 

4.  What  is  the   cost  of  gas 
registered    by    this   meter    at 
85  cts.  per  1000  cu.  ft.? 

How  to  Read  an  Electric  Meter 

(See  the  subject  of  the  electricity  in  the  Appendix) 

There  are  three  terms  used  in  connection  with  electricity 
which  it  is  important  to  understand ;  namely,  the  volt,  the 
ampere,  and  the  watt  or  kilowatt. 

(1)  The  volt  is  the  unit  of  Electromotive  Force  or  electrical 
pressure.     It  is  the  pressure  necessary  to  force  a  current  of 
one  ampere  through  a  resistance  of  one  ohm. 

(2)  The  unit  of  electric  current  strength  is  the  ampere.     It 


170       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

is  the  amount  of  current  flowing  through  a  resistance  of  one 
ohm  under  a  pressure  of  one  volt. 

(3)  The  watt  is  the  unit  of  electrical  power  ;  it  is  the  prod- 
uct of  volts  (of  electromotive  force)  and  current  (amperes)  in 
the  circuit,  when  their  values  are  respectively  one  volt  and 
one  ampere.  That  is  to  say,  if  we  have  an  electrical  device 
operated  at  3  amperes,  on  a  line  voltage  of  115  volts,  the 
amount  of  current  consumed  is  equal  to  115  x  3  =  345  watts, 
which,  if  operated  continuously  for  one  hour,  will  register  on 
the  electric  meter  as  345  watt  hours,  or  .345  kilowatt  hours 
(a  kilowatt  hour  being  equal  to  1000  watt  hours). 

All  electrically  operated  devices  are  stamped  with  the  ampere  and 
voltage  rating.  This  stamping  may  be  found  on  the  name-plate  or  bottom 
of  the  device.  By  multiplying  the  voltage  of  the  circuit  upon  which  the 
device  is  to  be  operated  by  the  amperes  as  found  stamped  on  the  device, 
we  can  quickly  determine  the  wattage  consumption  of  the  latter,  as  ex- 
plained under  the  definition  of  the  watt,  and  as  shown  above.  The  line 
voltage  which  is  most  extensively  supplied  by  Electric  Lighting  com- 
panies in  this  country  is  115  volts,  and  where  this  voltage  is  in  operation, 
the  devices  are  stamped  for  voltage  thus:  V.  110-125.  This  means 
that  the  device  may  be  used  on  a  circuit  where  the  voltage  does  not  drop 
below  110  volts  or  rise  above  125  volts.  By  operating  a  device  with  the 
above  stamping  on  a  circuit  of  106  volts  the  life  of  the  device  would  be 
very  much  longer,  but  the  results  desired  from  it  would  be  secured  much 
more  slowly.  Again,  if  the  same  device  were  used  on  a  circuit  oper- 
ating at  130  volts,  the  life  of  the  device  would  be  very  short,  although  the 
results  desired  from  it  would  be  brought  about  much  more  quickly.  Be- 
fore attempting  to  operate  an  electrically  heated  or  lighted  device,  if  in 
doubt  about  the  voltage  of  the  circuit,  it  is  best  to  call  upon  the  Electric 
Company  with  which  you  are  doing  business  and  ask  the  voltage  of  their 
lines. 

Incandescent  electric  lamps,  while  known  to  the  average  user  as 
lamps  of  a  certain  "candle-power,"  are  all  labeled  with  their  proper 
wattage  consumption.  Mazda  lamps,  suitable  for  household  use  and 
obtainable  at  all  lighting  companies,  are  made  in  15,  25,  40,  60,  and  100 
watt  sizes.  For  commercial  use,  lamps  of  1000  watts  and  known  as  the 
nitrogen-filled  lamps  are  on  the  market.  Nitrogen  lamps  are  made  in 
sizes  of  200  watts  and  upwards. 


HEAT  AND   LIGHT  171 

The  rate  by  which  current  consumed  for  lighting  and  small  heating  is 
figured  in  some  cities  is  known  as  the  "sliding  scale  rate,"  and  current 
is  charged  for  each  month,  as  follows  : 

The  first  200  kw.  hrs.  used  @  10^  per  kilowatt  hour. 
The  next  300  kw.  hrs.  used  @  8^  per  kilowatt  hour. 
The  next  500  kw.  hrs.  used  @  7  0  per  kilowatt  hour. 
The  next  1000  kw.  hrs.  used  @  6  ^  per  kilowatt  hour. 
The  next  3000  kw.  hrs.  used  @  5  ^  per  kilowatt  hour. 
All  over  5000  kw.  hrs.  used  @  4  ^  per  kilowatt  hour. 

Less  5%  discount,  if  bill  is  paid  within  15  days  from  date  of  issue. 

Under  the  sliding-scale  rate  the  more  electricity  that  is  consumed,  the 
cheaper  it  becomes.  But  it  is  also  readily  seen  that  the  customer  who 
uses  a  large  amount  of  electricity  pays  in  exactly  the  same  way  as  the 
small  consumer  pays  for  his  consumption. 

If  a  person  uses  less  than  200  kw.  hrs.  per  month,  he  pays  for  his  con- 
sumption at  the  rate  of  10  ^  per  kilowatt  hour  ;  if  he  uses  201  kw.  hrs.  of 
electricity  per  month,  he  pays  for  his  first  200  kw.  hrs.  at  the  first  step, 
namely  10  ^,  and  for  the  remaining  1  kw.  hr.  he  pays  8  fi  per  kilowatt 
hour. 

If  a  meter  reads  "  1000  kw.  hrs.,"  the  bill  is  not  figured  at  6^  direct, 
but  must  be  figured  step  by  step  as  shown  in  the  examples  below. 

For  convenience  in  figuring,  the  amount  of  power  used  by  various 
electrically  operated  devices  is  given  in  the  following  table.  By  figuring 
the  cost  of  each  per  hour,  it  will  be  seen  that  these  electric  servants  work 
very  cheaply. 


APPARATUS  WATTS  USED 


WHAT  is  COST 
PER  HOUR  1 


(a)  Disk  stove  200    •  ? 

(&)  6  Ib.  iron  440  ? 

(c)  Air  heater,  small  1000  ? 

(d)  Toaster-stove  500  ? 

(e)  Heating  pad  55  ? 
(/)  Sewing-machine  motor  50  (average)  ? 
(#)  25  watt  (16  c  p.)  lamp  25  ? 
(ft)  Chafing  dish  500  ? 
(0  Washing-machine  motor  200  (average)  ? 

EXAMPLE.  —  Suppose  a  customer  in  one  month  used   6120 
kilowatt  hours  of  electricity,  what  is  the  amount  of  his  bill 
1  Based  on  10  cents  per  kilowatt  hour. 


172       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

with   5  %  deducted   if  the   bill   is   paid  within  the  discount 
period  of  15  days  from  date  of  issue  ? 

SOLUTION.  —        6120  kw.  hrs.  =  total  amount  used. 

First  200  kw.  hrs.  @  10^  =  $   20.00 

5920 
Next  _300kw.  hrs.  @    8?=      24.00 

5620 
Next  500  kw.  hrs.  @    7  /  =      35.00 

5120 
Next  1000  kw.  hrs.  @    §t=      60.00 

4120 
Next  3000  kw.  hrs.  @    5/=     150.00 

We  have  now  figured  for  5000  kw.  hrs.,  and  as  our  rate  states  that  all 
over  5000  kw.  hrs.,  is  figured  at  4  ^  per  kilowatt  hours,  we  have 

1120  kw.  hrs.  @    4?  =  $   44.80 

$333.80  =  gross  bill 

Assuming  that  the  bill  is  paid  within  the  given  discount  period,  we 
deduct  5  %  from  the 

gross  bill,  which  equals  I   16.69 

$317. 11  =  net  bill 

EXAMPLES 

1.  A  customer  uses  in  one  month  300  kw.  hr.  of  electricity. 
What  is  the  amount  of  his  bill  if  5  %  is  deducted  for  payment 
within  15  days  ? 

2.  What  is  the  amount  of  bill,  with  5  %  deducted,  for  15 
kw.  hr.  of  electricity  ? 

An  electric  meter  is  read  in  the  same  way  that  a  gas  meter  is  read. 
In  deciding  the  reading  of  a  pointer,  the  pointer  before  it  (to  the  right) 
must  be  consulted.  Unless  the  pointer  to  the  right  has  reached  or  passed 
zero,  or,  in  other  words,  completed  a  revolution,  the  other  has  not  com- 
pleted the  division  upon  which  it  may  appear  to  rest.  Figure  1  reads 
11  kw.  hrs.,  as  the  pointer  to  the  extreme  right  has  made  one  complete 
revolution,  thus  advancing  the  second  pointer  to  the  first  digit  and  has 
itself  passed  the  first  digit  on  its  dial. 


HEAT  AND  LIGHT 


173 


FIG.  1.  —  READING  11  KW.  MRS. 


Fia.  2.  —  WHAT  is  THE  READING? 


Q/r^>\ 
f     ¥ "     \ 


ILOWATT-  HOUC.S 


FIG.  3.  —  READING  424  KW.  HRS. 


FIG.  4.  — WHAT  is  THE  READING? 


FIG.  5.  —  WHAT  is  THE  READING  ? 


174        VOCATIONAL  MATHEMATICS  FOR   GIRLS 

1.  What  is  the  cost  of  electricity  in  Fig.  1,  using  the  rates 
on  page  171  ? 

2.  What  is  the  cost  of  electricity  in  Fig.  2,  using  the  rates 
on  page  171,  with  the  discount  ? 

3.  What  is  the  cost  of  electricity  in  Fig.  3,  using  the  rates 
on  page  171,  with  the  discount  ? 

EXAMPLES 

1.  What  is  the  cost  of  maintaining  ten  25-watt  Mazda  lamps, 
burning  30  hours  at  10  cents  per  kw.  hr.  ? 

2.  What  will  it  cost  to  run  a  sewing  machine  by  a  motor 
(50  watts)  for  15  hours  at  9  cents  per  kw.  hr.  ? 

3.  A  6-lb.  electric  flatiron  is  marked  110  V.  and  4  amperes. 
What  will  it  cost  to  use  the  iron  for  20  hours  at  8  cents  per 
kw.  hr.  ? 

4.  An    electric    washing    machine    is    marked    110   V.    and 
2  amperes.     What  will  it  cost  to  run  it  15  hours  at  81  cents 
per  kw.  hr.  ? 

5.  An  electric  toaster  stove  is  marked  115  volts  and  3J  am- 
peres.    What  will  it  cost  to  run  it  for  a  month  (thirty  break- 
fasts)  15   hours  at  8J  cents   per  kw.  hr.  ?     If  a  discount  of 
5  %  is  allowed  for  prompt  payment,  what  is  the  net  amount 
of  the  bill  ? 

Methods  of  Heating 

Houses  are  heated  by  hot  air,  hot  water,  or  steam.  In  the 
hot-water  system  of  heating,  hot  water  passes  through  coils 
of  pipes  from  the  heater  in  the  basement  to  radiators  in  the 
rooms.  The  water  is  heated  in  the  boiler,  and  the  portion  of 
the  fluid  heated  expands  and  is  pushed  upward  by  the  adjacent 
colder  water.  A  vertical  circulation  of  the  water  is  set  up 
and  the  hot  water  passes  from  the  boiler  to  the  radiators  and 
gives  off  its  heat  to  the  radiators,  which  in  turn  give  it  off  to 
the  surrounding  air  in  the  room.  The  convection  currents 


HEAT  AND   LIGHT 


175 


carry  heat  through  the  room  and  at  the  same  time  provide  for 
ventilation. 

In  the  hot-air  method  the  heat  passes  from  the  furnace 
through  openings  in  the  floor  called  registers.  This  method 
frequently  fails  to  heat 
a  house  uniformly  be- 
cause there  is  no  way  for 
the  air  in  certain  rooms 
to  escape  so  as  to  per- 
mit fresh  and  heated 
air  to  enter. 

Steam  heating  consists 
in  allowing  steam  from 
a  boiler  in  the  basement 
to  circulate  through  coils 
or  radiators.  The  steam 

gives  off  its  heat  to  the 

HOT  AIR  HEATING  SYSTEM 
radiators,  which  in  turn 

give  it  off  to  the  surrounding  air. 

Room-heating  Calculations 


In  order  to  insure  comfort 
and  health,  every  housewife 
should  be  able  to  select  an 
efficient  room-heating  appli- 
ance, or  be  able  to  tell  whether 
the  existing  heating  appara- 
tus is  performing  the  required 
service  in  the  most  econom- 
ical manner.  In  order  to  do 
this,  it  is  necessary  to  know 
how  to  determine  the  re- 
quirements for  individual 
room  heating. 


HOT  WATER  HEATING  SYSTEM 


176       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

For  Steam  Heating 

Allow  1  sq.  ft.  of  radiator  surface  for  each 
80  cu.  ft.  of  volume  of  room. 
13  sq.  ft.  of  exposed  wall  surface. 
3  sq.  ft.  of  exposed  glass  surface  (single  window). 
6  sq.  ft.  of  exposed  glass  surface  (double  window). 
For  Hot-water  Heating 

Add  50  per  cent  to  the  amount  of  radiator  surface  obtained  by  the 
above  calculation. 

For  Gas  Heaters  having  no  Flue  Connection 
Allow  1  cu.  ft.  of  gas  per  hour  for  each 
215  cu.  ft.  of  volume  of  room. 
35  sq.  ft.  of  exposed  wall  surface. 
9  sq.  ft.  of  exposed  glass  surface  (single  window). 
18  sq.  ft.  of  exposed  glass  surface  (double  window) . 

The  results  obtained  must  be  further  increased  by  one  or  more  of  the 
following  factors  if  the  corresponding  conditions  are  present. 

Northern  exposure        1.3 

Eastern  or  western  exposure 1.2 

Poor  frame  construction        2.5 

Fair  frame 2.0 

Good  frame  or  12-inch  brick 1.2 

Room  heated  in  day  time  only 1.1 

Room  heated  only  occasionally 1.3-1.4 

Cold  cellar  below  or  attic  above     .     .     .     .     .  1.1 

EXAMPLE.  —  How  much  radiating  surface,  for  steam  heating, 
is  necessary  to  heat  a  bathroom  containing  485  cu.  ft.  ?  The 
bathroom  is  on  the  north  side  of  the  house. 

-4F8ff5-  =  6^  sq.  ft.  of  radiating  surface 
6TV  X  1.3  =  ft  x  ft  =  7tfi  sq.  ft. 
6%  +  7|ft  =  6TVo  +  7  J|i  =  13}f£  sq.  ft.  or  approx.  14  sq.  ft.    Ans. 

EXAMPLES 

1.  How  much  radiating  surface,  for  steam   heating,  is  re- 
quired for  a  bathroom  12'  X  6'  x  10'  on  an  eastern  exposure  ? 

2.  How  much  radiating   surface,  for   hot-water  heating,  is 
required  for  the  bathroom  in  example  1  ? 


COST   OF   FURNISHING   A   HOUSE  177 

3.  How  large  a  gas  heater  should  be  used  for  heating  the 
bathroom  in  example  1  ? 

4.  (a)  How  much  radiating  surface  is  required  for  steam 
heating,  in  a  living  room  18'  x  16^'  x  10',  with  three  single 
windows  2'  x  5^ '  ?     The  room  is  exposed  to  the  north. 

(6)  How  much  radiating  surface  for  hot- water  heating  ? 
(c)  How  much  gas  should  be  provided  to  heat  the  room  in 
example  (a)  ? 

5.  (a)  How  much  radiating  surface  is  required  for  steam 
heating  a  bedroom  19'  x  17'  x  11'  with  two  single  windows 
2'  x  5y  ?     The  house  is  of  poor  frame  construction. 

(b)  How  much  radiating  surface  for  hot- water  heating  ? 

(c)  How  much  gas    should   be   provided   to   heat   room   in 
example  (a)  ? 


CHAPTER   VIII 
THRIFT  AND  INVESTMENT 

IT  is  not  only  necessary  to  increase  your  earning  capacity,  but 
also  to  develop  systematically  and  regularly  the  saving  habit. 
A  dollar  saved  is  much  more  than  two  dollars  earned.  For  a 
dollar  put  at  interest  is  a  faithful  friend,  earning  twenty-four 
hours  a  day,  while  a  spent  dollar  is  like  a  lost  friend  —  gone 
forever.  Histories  of  successful  men  show  that  fortune's 
ladder  rests  on  a  foundation  of  small  savings ;  it  rises  higher 
and  higher  by  the  added  power  of  interest.  The  secret  of 
success  lies  in  regularly  setting  aside  a  fixed  portion  of  one's 
earnings,  for  instance  10  %  ;  better  still,  10  %  for  a  definite 
object,  such  as  a  home  or  a  competency. 

In  every  community  one  will  find  various  agencies  by  which 
savings  can  be  systematically  encouraged  and  most  success- 
fully promoted.  These  institutions  promote  habits  of  thrift, 
encourage  people  to  become  prudent  and  wise  in  the  use  of 
money  and  time.  They  help  people  to  buy  or  build  homes  for 
themselves  or  to  accumulate  a  fund  for  use  in  an  emergency  or 
for  maintenance  in  old  age. 

Banks 

Working  people  should  save  part  of  their  earnings  in  order  to  have 
something  for  old  age,  or  for  a  time  of  sickness,  when  they  are  unable  to 
work.  This  money  is  deposited  in  banks  —  savings,  National,  cooper- 
ative, and  trust  companies. 

National  Banks 

National  banks  pay  no  interest  on  small  deposits,  but  give  the  depositor 
a  check  book,  which  is  a  great  convenience  in  business.  National  banks 
require  that  a  fixed  sum  should  be  left  on  deposit,  $  100  or  more,  and 
some  of  them  charge  a  certain  amount  each  month  for  taking  care  of  the 
money. 

178 


THRIFT   AND    INVESTMENT  179 

Trust  Companies 

Trust  companies  receive  money  on  deposit  and  allow  a  customer  to 
draw  it  out  by  means  of  a  check.  They  usually  pay  a  small  interest  on 
deposits  that  maintain  a  balance  over  $  500. 

Cooperative  Banks 

When  a  person  takes  out  shares  in  a  cooperative  bank,  he  pledges  him- 
self to  deposit  a  fixed  amount  each  month.  If  he  deposits  $5,  he  is  said 
to  have  five  shares.  No  person  is  permitted  to  have  more  than  twenty- 
five  shares.  The  rate  of  interest  is  much  higher  than  in  other  banks,  and 
when  the  shares  mature,  which  is  usually  at  the  end  of  about  eleven 
years,  all  the  money  must  be  taken  out.  Many  people  build  their  home 
through  the  cooperative  bank,  for,  like  every  other  bank,  it  lends  money. 
When  a  person  borrows  money  from  a  cooperative  bank,  he  has  to  give  a 
mortgage  on  real  estate  as  security,  and  must  pay  back  a  certain  amount 
each  month. 

Savings  Banks 

The  most  common  form  of  banking  is  that  carried  on  by  the  Savings 
Sank.  People  place  their  money  in  a  savings  bank  for  safe  keeping  and 
for  interest.  The  bank  makes  its  money  by  lending  at  a  higher  interest 
than  it  pays  its  depositors.  There  is  a  fixed  date  in  each  bank  when 
money  deposited  begins  to  draw  interest.  Some  banks  pay  quarterly  and 
some  semi-annually.  At  different  times  banks  pay  different  rates  of 
interest;  and  often  in  the  same  community  there  are  different  rates  of  in- 
terest paid  by  different  banks. 

Every  bank  is  obliged  to  open  its  books  for  inspection  by  special 
officers  who  are  appointed  for  that  work.  If  these  men  did  their  work 
carefully  and  often  enough,  there  would  be  almost  no  chance  of  loss  in 
putting  money  in  a  bank.  Banks  fail  when  they  lend  money  to  too  many 
people  who  are  unable  to  pay  it  back. 

EXAMPLES 

(Review  interest  on  page  50) 

1.  I  place  $  400  in  a  savings  bank  that  pays  4  %  on  Jan.  1, 
1916.     Money  goes  on  interest  April  1  and  at  each  successive 
quarter.     How  much  money  have  I  to  my  credit  at  the  begin- 
ning of  the  third  quarter  ? 

2.  A  man  with  a  small  business  places  his  savings,  $  1683, 


180       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

in  a  trust  company  so  he  can  pay  his  bills  by  check.  The 
bank  pays  2  %  for  all  deposits  over  $  500.  He  draws  checks 
for  $  430  and  $  215  within  a  few  days.  At  the  end  of  a 
month  he  will  receive  how  much  interest  ? 

3.  Practically  10  %  of  the  entire  population  of  the  United 
States,  including  children,  have  savings-bank  accounts.     If  the 
population  is  92,818,726,  how  many  people  have  savings  bank 
deposits  ? 

4.  On  April  1,  1910,  a  woman  deposited  $  513  in  a  savings 
bank  which  pays  4  %  interest.     Interest  begins  April  1  and  at 
each  succeeding  quarter.     Dividends  are  declared  Jan.  1  and 
July  1.     What  is  the  total  amount  of  her  deposit  at  the  present 
date? 

The  savings  bank  is  not  adapted  to  the  needs  of  those  with  large  sums 
to  place  at  interest.  It  is  a  place  where  small  sums  may  be  deposited 
with  absolute  safety,  earn  a  modest  amount,  and  be  used  by  the  depositor 
at  short  notice.  The  savings  bank  lends  money  on  mortgages  and  re- 
ceives about  5  °fo.  It  pays  its  depositor  either  3£  %  or  4  %.  The  differ- 
ence goes  to  pay  expenses  and  to  provide  a  surplus  fund  to  protect 
depositors. 

The  question  may  be  asked,  "  Why  cannot  the  ordinary  depositor  lend 
his  money  on  mortgages  and  receive  5  °fo  ?  "  He  can,  if  he  is  willing  to 
assume  the  risk.  When  you  receive  4  %  interest,  you  are  paying  1%  to 
1|  °fo  in  return  for  absolute  safety  and  freedom  from  the  necessity  of 
selecting  securities. 

Mortgages 

A  mortgage  is  the  pledging  of  property  as  a  security  for  a  debt.  Mr. 
Allen  owns  a  farm  and  wants  some  money  to  buy  cattle  for  it.  He  goes 
to  Mr.  Jones  and  borrows  $  1000  from  him,  and  Mr.  Jones  requires  him 
to  give  as  surety  a  mortgage  on  his  farm.  That  is,  Mr.  Allen  agrees  that 
if  he  does  not  pay  back  the  $ 1000,  the  farm,  or  such  part  as  is  necessary 
to  cover  the  debt,  shall  belong  to  Mr.  Jones. 

Under  present  law,  if  a  man  wishes  to  foreclose  a  mortgage,  —  that  is, 
compel  its  payment  when  due,  —  he  cannot  take  the  property,  but  it  must 
be  sold  at  public  auction.  From  the  money  received  at  the  sale  the  man 
who  holds  the  mortgage  receives  his  full  amount,  and  anything  that  is 
left  belongs  to  the  man  who  owned  the  property. 


THRIFT   AND    INVESTMENT  181 

Notes 

A  promissory  note  is  a  paper  signed  by  the  borrower  promising  to 
repay  borrowed  money.  Notes  should  state  value  received,  date,  the 
amount  borrowed  (called  the  face),  the  rate,  to  whom  payable,  and 
the  time  and  place  of  payment.  Notes  are  due  at  the  expiration  of 
the  specified  time. 

The  rate  of  interest  varies  in  different  parts  of  the  country.  The 
United  States  has  to  pay  about  2  % .  Savings  banks  pay  3  %  or  4  °fo . 
Individuals  borrowing  on  good  security  pay  from  4  %  to  6  °fo. 

In  order  to  make  the  one  who  loans  the  money  secure,  the  borrower, 
called  the  maker  of  the  note,  often  has  to  get  a  friend  to  indorse  or  sign 
this  note.  The  indorser  must  own  some  sort  of  property  and  if,  at  the 
end  of  six  months  or  the  time  specified,  the  maker  cannot  pay  the  note, 
he  is  notified  by  written  order,  called  a  protest,  and  may,  later,  be  called 
upon  to  repay  the  note. 

A  man  is  asking  a  great  deal  when  he  asks  another  man  to  sign  a  note 
for  him.  Unless  you  have  more  money  than  you  need,  it  is  better  busi- 
ness policy  to  refuse  the  favor. 

Always  be  sure  that  you  know  exactly  what  you  are  signing  and  that 
you  know  the  responsibility  attached.  If  you  are  a  stenographer  or  a 
clerk  in  an  office,  you  will  often  be  called  upon  to  witness  a  signature  and 
then  to  sign  your  own  name  to  prove  that  you  have  witnessed  it.  Always 
insist  upon  reading  enough  of  the  document  to  be  sure  that  you  know 
just  what  your  signature  means. 

EXAMPLES 

1.  My  house  is  worth  $4000  and  the  bank  holds  a  mortgage 
on  it  for  one-half  its  value.     They  charge  5  %  interest,  which 
must  be  paid  semi-amiually.     How  much  do  I  pay  each  time  ? 

2.  A  bank  holds  a  mortgage  of  $  2500  on  a  house.     The  in- 
terest is  5  %  payable  semi-annually.     How  much  is  paid  for 
interest  at  the  end  of  three  years  ? 

3.  A  man  buys  property  worth  $  3000.     He  gives  a  $  2000 
mortgage  and  pays  5-J-  %  interest.     What  will  be  the  interest 
on  the  mortgage  at  the  end  of  the  year  ?     Suppose  he  does  not 
pay  the  interest,  how  long  can  he  hold  the  property  ? 


182       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

DIFFERENT  KINDS  OF  PROMISSORY  NOTES 
$_  Montgomery,  Ala — 

after  date  for  value  received ^promise 


to  pay  to  the  order  of 


.Dollars 


at  fHed)amc0  National 
No 


A  COMMON  NOTE 

St.  Paul,  Minn 19 

.after  date  for  value  received  we  jointly  and 


severally  promise  to  pay  to  the  order  o 


.Dollars 


at  $fledjamc0  National  Bank. 
No.  _          _  Due 


JOINT  NOTE 

$ FALL  RIVER,  MASS. 191 

after  date  for  value  received 

promise  to  pay  to  the  order  of  THE  MECHANICS  NATIONAL  BANK  of  Fall  River, 

Mass.  _        DOLLARS, 

at  said  Bank,  and  interest  for  such  further  time  as  said  principal  sum  or  any 

part  thereof  shall  remain  unpaid  at  the  rate  of per  cent  per  annum, 

having  deposited  with  the  said  Mechanics  National  Bank,  as  GENERAL  COL- 
LATERAL SECURITY,  for  the  payment  of  any  of liabilities  to  said 

Bank  due,  or  to  become  due,  direct  or  indirect,  joint  or  several,  individual  or 
firm,  now  or  hereafter  contracted  or  incurred,  at  the  option  of  said  Bank, 
the  following  property,  viz.  : 


and hereby  authorize  said  Bank  or  its  assigns  to  sell  and  transfer  said 

property  or  any  part  thereof  without  notice,  at  public  or  private  sale,  at  the 


THRIFT   AND    INVESTMENT  183 

option  of  said  Bank  or  its  assigns,  on  the  non-payment  of  any  of  the  liabili- 
ties aforesaid,  and  to  apply  the  proceeds  of  said  sale  or  sales,  after  deducting 
all  the  expenses  thereof,  interest,  all  costs  and  charges  of  enforcing  this 
pledge  and  all  damages,  to  the  payment  of  any  of  the  liabilities  aforesaid, 

giving credit  for  any  balanqe  that  may  remain.     Said  Bank  or  its 

assigns  shall  at  all  times  have  the  right  to  require  the  undersigned  to  deposit 
as  general  collateral  security  for  the  liabilities  aforesaid,  approved  additional 

securities  to  an  amount  satisfactory  to  said  Bank  or  its  assigns,  and 

hereby  agree  to  deposit  on  demand  (which  may  be  made  by  notice  in  writing 

deposited  in  the  post  office  and  addressed  to at last   known 

residence  or  place  of  business)  such  additional  collateral.  Upon fail- 
ing to  deposit  such  additional  security,  the  liabilities  aforesaid  shall  be  deemed 
to  be  due  and  payable  forthwith,  anything  hereinbefore  or  elsewhere  ex- 
pressed to  the  contrary  notwithstanding,  and  the  holder  or  holders  may 
immediately  reimburse  themselves  by  public  or  private  sale  of  the  security 
aforesaid;  and  it  is  hereby  agreed  that  said  Bank  or  any  of  its  officers, 
agents,  or  assigns  may  purchase  said  collateral  or  any  part  thereof  at  such 
sale.  In  case  of  any  exchange  of  or  addition  to  the  above  described  collateral, 
the  provisions  hereof  shall  apply  to  said  new  or  additional  collateral. 


COLLATERAL  NOTE 

4.  On  Jan.  2,  1915,  Mr.  Lewis  gave  his  note  for  $2400, 
payable  on  Feb.  27,  with  interest  at  6  %.  On  Feb.  2,  he  paid 
$  600.  How  much  was  due  Mar.  2,  1915  ? 

SOLUTION.  —  In  the  case  of  notes  running  for  less  than  a  year,  exact 
days  are  counted  ;  from  Jan.  2  to  Feb.  2  is  31  days. 

Interest  Jan.  2  to  Feb.  2,  31  days, 

$  12.00    for  30  days 
.40    for    1  day 
.$  12.40  31  days 

Amount  due  Feb.  2,        $  2400  +  12.40  =  $  2412.40. 
$  2412.40  -  600  =  $  1812.40. 

Interest  Feb.  2  to  March  2,  28  days, 

§6.0413  20  days 

1.8124  6  days 

.6041  2  days 

$8.4578  or  $8.46 

1812.40 

Amount  due  March  2,  $  1820.86    Ans. 


184       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

Money  lenders  may  discount  their  notes  at  banks  and  thus  obtain  their 
money  before  the  note  comes  due.  But  the  banks,  in  return  for  this  serv- 
ice, deduct  from  the  full  amount  of  the  note  interest  at  a  legal  rate  on 
the  full  amount  for  such  time  as  remains  between  the  day  of  discount 
and  the  day  when  the  note  comes  due. 

To  illustrate  :  A  man  has  a  note  for  $  600  due  in  three  months  at  6  % 
interest.  At  the  end  of  a  month  he  presents  the  note  at  a  bank  and 
returns  the  difference  between  the  amount  at  maturity,  $  609,  and  the 
interest  on  $609  for  two  months,  the  remaining  time,  at  legal  rate  6%, 
$6.09  or  $609  -  6.09  =  $602.91. 

5.  On  June  1,  1914,  Mr.  Smith  gives  his  note  for  $  1200, 
payable  on  demand  with  interest  at  6%.     The  following  pay- 
•ments  are  made  on  the  note  :  Aug.  1, 1914,  $  140 ;  Oct.  1, 1914, 
$100;  Dec.  1,  1914,  $100;   and  Feb.  1,  1914,  $160.     How 
much  was  due  May  1,  1915  ? 

6.  A  merchant  buys  paper  amounting  to  $  945.     He  gives 
his  note  for  this  amount,  payable  in  three   months  at  6  % . 
The  paper  dealer  desires  to  turn  the  note  into  cash  immedi- 
ately.    He  therefore  discounts  it  at  the  bank  for  6  % .     How 
much  does  he  receive  ? 

Stocks 

It  often  happens  that  one  man  or  a  group  of  men  desire  to  engage  in  a 
business  that  requires  more  money  than  they  alone  are  able  or  willing  to 
invest  in  it.  They  obtain  more  money  by  organizing  a  stock  company, 
in  which  they  themselves  buy  as  many  shares  as  they  choose,  and  then 
they  induce  others  to  pay  for  enough  more  shares  to  make  up  the  capital 
that  is  needed  or  authorized  for  the  business. 

A  stock  company  consists  of  a  number  of  persons,  organized  under  a 
general  law  or  by  special  charter,  and  empowered  to  transact  business  as 
a  single  individual.  The  capital  stock  of  a  company  is  the  amount  named 
in  its  charter.  A  share  is  one  of  the  equal  parts  into  which  the  capital 
stock  of  a  company  is  divided  (generally  $  100). 

The  par  value  of  a  share  of  stock  is  its  original  or  face  value  ;  the 
market  value  of  a  share  of  stock  is  the  price  for  which  the  share  will  sell 
in  the  market.  The  market  values  of  leading  stocks  vary  from  day  to 
day,  and  are  quoted  in  the  daily  papers;  e.g.  "N.  Y.  C.,  131"  means 
that  the  stock  of  the  New  York  Central  R.  R.  Co.  is  selling  to-day  at 
$  131  a  share. 


THRIFT   AND    INVESTMENT 


185 


Dividends  are  the  net  profits  of  a  stock  company  divided  among  the 
stockholders  according  to  the  amount  of  stock  they  own. 

Stock  companies  often  issue  two  kinds  of  stock,  namely  :  preferred 
stock,  which  consists  of  a  certain  number  of  shares  on  which  dividends 
are  paid  at  a  fixed  rate,  and  common  stock,  which  consists  of  the  re- 
maining shares,  among  which  are  apportioned  whatever  profits  there  are 
remaining  after  payment  of  the  required  dividends  on  the  preferred  stock. 


CAZENDV1A  NATIONAL  BANK 


CERTIFICATE  OF  STOCK 


Stocks  are  generally  bought  and  sold  by  brokers,  who  act  as  agents 
for  the  owners  of  the  stock.  Brokers  receive  as  their  compensation  a 
certain  per  cent  of  the  par  value  of  the  stock  bought  or  sold.  This  is 
called  brokerage.  The  usual  brokerage  is  |  %  of  the  par  value  ;  e.g.  if  a 
broker  sells  10  shares  of  stock  for  me,  his  brokerage  is  |  °/o  of  $  1000,  or 
$1.25. 

EXAMPLE.  —  What  is  the  cost  of  20  shares  of  No.  Butte  301  ? 

$  30^  +  $  \  i  =  $  30|,  cost  of  1  share. 

X  20  =  $600  +  $  12£  =  §612.50,  total  cost. 


i  of  1  %  of  $  100  =  1  of  $1,  broker's  charge  per  share. 


186       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

EXAMPLES 

1.  The    par    value    of    a    certain    stock    is    $  100.      It    is 
quoted   on    the    market  at  $  87|-..     What  is  the  difference  in 
price    per    share    between    the    market   value    and   the   par 
value  ? 

2.  What  is  the  cost  of  40  shares  of  Copper  Range  at  53  ? 

3.  What  is  the  cost  of  53  shares  of   Calumet  and  Hecla 
at  680  ? 

4.  I  have  50  shares  of  Anaconda.     How  much  shall  I  re- 
ceive if  I  sell  at  661  ? 

5.  I  buy  60  shares  of  Anaconda  at  66J.     It  pays  a  quarterly 
dividend  of   $  1.50.     What   interest   am  I   receiving   on   my 
money  ? 

Bonds 

Corporations  and  national,  state,  county,  and  town  governments  often 
need  to  borrow  money  in  order  to  meet  extraordinary  expenditures. 
When  a  corporation  wishes  to  borrow  a  large  sum  of  money  for  several 
years,  it  usually  mortgages  its  property  to  a  person  or  bank  called  a  trustee. 
The  amount  of  the  mortgage  is  divided  into  parts  called  bonds,  and  these 
are  sold  to  investors.  The  interest  on  the  bonds  is  at  a  fixed  rate  and  is 
generally  payable  semi-annually.  Shares  of  stock  represent  the  property 
of  a  corporation,  while  bonds  represent  debts  of  the  corporation ;  stock- 
holders are  owners  of  the  property  of  the  corporation,  while  bondholders 
are  its  creditors. 

Bonds  of  large  corporations  whose  earnings  are  fairly  stable  and  regu- 
lar, like  steam  railroads,  street  railways,  and  electric  power  and  gas 
plants,  whose  property  must  be  employed  for  public  necessities  regardless 
of  the  ability  of  the  managers,  are  usually  good  investments.  Well-secured 
bonds  are  safer  than  stocks,  as  the  interest  on  the  bonds  must  be  paid  re- 
gardless of  the  condition  of  the  business. 

For  the  widow  who  is  obliged  to  live  on  the  income  from  a  moderate 
amount  of  capital,  it  is  better  to  invest  in  bonds  and  farm  mortgages  than 
in  stock. 


THRIFT  AND   INVESTMENT 


187 


A  SAMPLE  BOND 


188       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

EXAMPLES 

1.  A  man  put  $  200  in  the  Postal  Savings  Bank  and  received 
2  %    interest.     What  would  have  been  the  difference  in  his 
income  for  a  year  if  he  had  taken  it  to  a  savings  bank  that 
paid  3|  %  ? 

2.  A  widow  had  a  principal  of  $  18,000.     She  placed  it  in  a 
group  of  savings  banks  that  paid  3f  %,.     The  next  year  she 
purchased  farm  mortgages  and  secured  51  %.     What  was  the 
difference  in  her  income  for  the  two  years  ? 

3.  Two  sons  were  left  $  15,000  each.     One  placed  it  in  first- 
class  bonds  paying  5^  %.     The  other  placed  it  in  savings  banks 
and  averaged  41  % .     WThat  was  the  difference  in  income  per 
year? 

Fire  Insurance 

Household  furniture,  books,  apparel.,  etc.,  can  be  insured  at  a  low  rate. 
While  it  will  not  make  a  man  less  careful  in  protecting  his  home  from  fire, 
it  will  make  him  more  comfortable  in  the  thought  that  if  fire  should  come, 
the  family  will  not  be  left  without  the  means  of  clothing  themselves  and 
refurnishing  the  house.  One  of  the  first  duties  then,  after  the  home  is 
established,  is  to  secure  insurance. 

Insurance  companies  issue  a  policy  for  1,  3,  or  5  years.  There  is  an 
advantage  in  buying  a  policy  for  more  than  one  year,  for  on  the  3-  or  5- 
year  policy  there  is  a  saving  of  about  20  %  in  premiums.  Rules  of  per- 
centage apply  to  problems  in  insurance. 

EXAMPLE.  —  A  house  worth  $  8400  is  insured  for  its  full 
value  at  28  cents  per  $  100.  WThat  is  the  cost  of  premium  ? 

SOLUTION. 

$  8400  is  the  value  of  the  policy  or  base. 

28  cents  is  the  rate  of  premium  or  rate. 

The  premium  or  interest  is  the  amount  to  be  found. 

84  x  $0.28  =  $23.52,  premium. 

EXAMPLES 

1.  Find  the  insurance  upon  a  dwelling  house  valued  at 
$  3800  at  $  2.80  per  $  1000  if  the  policy  is  on  80  %  of  the  value 
of  the  house. 


THRIFT   AND    INVESTMENT  189 

2.  Mr.  Jones  takes  out  $  800  insurance  on  his  automobile  at 
2  °fc .     What  is  the  cost  of  the  premium  ? 

3.  The  furniture  in  one  tenement  of  a  three-family  house  is 
valued  at  $  1000.     What  premium  is  paid,  if  it  is  insured  at 
the  rate  of  1  %  for  5  years  ? 

4.  If  the  premium  on  the  same  furniture  in  a  two-family 
house  in  a  different  city  is  $  7.50,  what  is  the  rate,  expressed 
in  per  cent  ? 

Life  Insurance 

Every  industrious  and  thrifty  person  lays  aside  a  certain  amount 
regularly  for  old  age  or  future  necessities,  or  in  case  of  death  to  provide 
sufficient  amount  for  the  support  of  the  family.  This  is  usually  done  by 
taking  out  life  insurance  from  a  corporation  called  an  insurance  company. 
This  corporation  is  obliged  to  obtain  a  charter  from  the  state,  and  is 
regularly  inspected  by  a  proper  state  officer. 

The  policy  or  contract  which  is  made  by  the  company  with  the  member, 
fixing  the  amount  to  be  paid  in  the  event  of  his  death,  is  called  a  life 
insurance  policy,  and  the  person  to  whom  the  amount  is  payable  is 
termed  the  beneficiary.  The  contribution  to  be  made  by  the  member  to 
the  common  fund,  as  stipulated  in  the  policy,  is  termed  the  premium,  and 
is  usually  payable  in  yearly,  half-yearly,  or  quarterly  installments. 

There  are  different  kinds  of  insurance  policies  :  the  simplest  is  the 
ordinary  life  policy.  Before  entering  into  a  contract  of  this  kind,  it 
is  necessary  to  fix  the  amount  of  the  premium,  which  must  be  large 
enough  to  enable  the  company  to  meet  the  necessary  expense  of  conduct- 
ing the  business  and  to  accumulate  a  fund  sufficient  to  pay  the  amount  of 
the  policy  when  the  latter  matures  by  the  death  of  the  insured. 

Making  the  Premium.  —  If  it  were  known  to  a  certainty  just  how  long 
the  policy  holder  would  live,  anyone  could  compute  the  amount  of  the 
necessary  premium.  Let  us  suppose,  for  illustration,  that  the  face  of  the 
policy  is  $  1000,  and  that  the  policyholder  will  live  just  twenty  years.  Let 
us  assume  that  the  business  is  conducted  without  expense,  and  that  the 
premiums  are  all  to  be  invested  at  interest  from  date  of  payment.  We 
do  not  know  to  a  certainty  what  rate  of  interest  can  be  earned  during  the 
whole  period,  and  we  shall  therefore  assume  one  that  we  can  safely 
depend  upon,  say  three  per  cent.  A  yearly  payment  of  .$36.13  invested 
at  three  per  cent  compound  interest  will  amount  to  $  1000  in  twenty 
years. 


190       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

No.  >213649  $5000 

gto*  fjmrtfe  #  tar  ptutttal  gif*  Iwstxmtxtje 
Cfompaug 

In  Consideration  of  the  application  for  this  Policy,  a  copy  of  which 
is  attached  hereto  and  made  a  part  hereof,  and  in  further  consideration  of 
the  payment  of 


ffiunflrrti  ffln'rtg^cight^  2^_  Dollars, 


100 

the  receipt  whereof  is  hereby  acknowledged,  and  of  the  &ttttuat  payment 
of  a  like  sum  to  the  said  Company,  on  or  before  the  __  day  of 

Januarg     jn  every  year  during  the  continuance  of  this  Policy,  promises 
to  pay  at  its  office  in  Milwaukee,  Wisconsin,  unto  _ 


_,  Beneficiar 2. 


of  gofrn  Boe—  _the  insured,  Of 


®cs  jffloines jn  t]ie  state  of. 


subject  to  the  rigfrt  of  the  gnstircfr,  frcrcfag  rcscrbcfr,  to  flange  the  33cncficiarg 
or  iScncficiarics  the  sum  of_  ^tbj ^Ti)ousanU—  ^Dollars, 

upon  receipt  and  approval  of  proof  of  the  death  of  said  Insured  while  this 
Policy  is  in  full  force,  the  balance  of  the  year's  premium,  if  any,  and  any 
other  indebtedness  on  account  of  this  Policy  being  first  deducted  there- 
from ;  provided,  however,  that  if  no  Beneficiary  shall  survive  the  said 
Insured,  then  such  payment  shall  be  made  to  the  executors,  administra- 
tors or  assigns  of  the  said  Insured. 

In  Witness  Whereof,  THE  NORTH  STAR  MUTUAL  LIFE  INSURANCE 
COMPANY,  at  its  office  in  Milwaukee,  Wisconsin,  has  by  its  President  and 

Secretary,  executed  this  contract,  this FirKt day  of January Qne 

thousand  nine  hundred  and sixteen.  — _ 


S.  A.  Hawkins,  Secretary.  L.  H.  Perkins,  President. 

ORDINARY  LIFE  INSURANCE  POLICY 


THRIFT   AND   INVESTMENT  191 

If  it  were  certain  that  the  policyholder  would  live  just  twenty  years, 
and  that  his  premiums  would  earn  just  three  per  cent  interest,  and  that 
the  business  could  be  conducted  without  expense,  the  necessary  premium 
would  be  $36.13.  But  there  are  certain  other  contingencies  that  should 
be  provided  for ;  such  as,  for  example,  a  loss  of  invested  funds,  or  a 
failure  to  earn  the  full  amount  of  three  per  cent  interest. 

To  meet  these  expenses  and  contingencies  something  should  be  added 
to  the  premium.  Let  us  estimate  as  sufficient  for  this  purpose  the  sum  of 
$7.  This  will  make  the  gross  yearly  premium  $43.13,  the  original  pay- 
ment ($36.13)  being  the  net  premium,  while  the  amount  added  thereto 
for  expenses,  etc.  ($7.00),  is  termed  the  loading. 

The  net  premium  is  the  amount  which  is  mathematically  necessary 
for  the  creation  of  a  fund  sufficient  to  enable  the  company  to  pay  the 
policy  in  full  at  maturity.  The  loading  is  the  amount  added  to  the  net 
premium  to  provide  for  expenses  and  contingencies.  The  net  premium 
and  loading  combined  make  up  the  gross  premium,  or  the  total  amount  to 
be  paid  each  year  by  the  insured. 

Mortality  Tables.  —  Although  it  is  impossible,  as  in  the  illustration 
given  above,  to  predict  in  advance  the  length  of  any  individual  life,  there 
is  a  law  governing  the  mortality  of  the  race  by  which  we  may  determine 
the  average  lifetime  of  a  large  number  of  persons  of  a  given  age.  We 
cannot  predict  in  what  year  the  particular  individual  will  die,  but  we  may 
determine  with  approximate  accuracy  how  many  out  of  a  given  number 
will  die  at  any  specified  age.  By  means  of  this  law  it  becomes  possible  to 
compute  the  premium  that  should  be  charged  at  any  given  age  with 
almost  as  much  exactness  as  in  the  example  given,  in  which  the  length  of 
life  remaining  to  the  individual  was  assumed  to  be  just  twenty  years. 

Let  us  suppose,  for  example,  that  observations  cover  a  period  of  time 
sufficient  to  include  the  history  of  100,000  lives.  Of  these,  you  will  find  a 
certain  number  dying  at  the  age  of  thirty,  a  larger  number  at  the  age  of 
forty,  and  so  on  at  the  various  ages,  the  extreme  limit  of  life  reached 
being  in  the  neighborhood  of  one  hundred  years.  The  mortuary  records 
of  other  groups  of  100,000.  living  where  conditions  are  practically  the 
same,  would  give  approximately  the  same  results — the  same  number  of 
deaths  at  each  age  in  100,000  born.  The  variation  would  not  be  great, 
and  the  larger  the  number  of  lives  under  observation,  the  nearer  the 
number  of  deaths  at  the  several  ages  by  the  several  records  would  ap- 
proach to  uniformity. 

In  this  manner  mortality  tables  have  been  constructed  which  show  how 
many  in  any  large  number  of  persons  born,  or  starting  at  a  certain  age, 
will  live  to  age  thirty,  how  many  to  age  forty,  how  many  to  any  other 


192       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

age,  and  likewise  the  number  that  will  die  at  each  age,  with  the  average 
lifetime  remaining  to  those  still  alive.  The  insurance  companies  from 
these  tables  construct  tables  of  premiums,  varying  according  to  the  amount 
and  kind  of  insurance  and  the  age  at  which  the  policy  is  taken  out. 

Kinds  of  Policies.  —  An  endowment  policy  is  essentially  for  persons  who 
must  force  themselves  to  save.  It  is  an  expensive  form  of  insurance,  but 
one  that  affords  the  young  man  or  woman  an  incentive  for  saving,  and 
that  matures  at  a  time  when  the  individual  has,  as  a  result  of  long 
experience,  better  opportunities  to  make  profitable  investments.  This 
policy  also  has  a  larger  loan  value  than  any  other,  and  this  sometimes  be- 
comes an  advantage  to  the  young  person.  However,  the  chief  advantage 
of  the  endowment  policy  is  its  incentive  to  save. 

A  limited  payment  policy,  such  as  the  twenty-payment  life,  appeals 
most  directly  to  those  who  desire  to  pay  for  life  insurance  only  within  the 
productive  period  of  their  life.  This  policy  should  attract  the  young  man 
who  is  uncertain  of  an  income  after  a  given  period,  or  who  does  not  wish 
insurance  premiums  to  be  a  burden  upon  him  after  middle  life.  Out  of 
the  relatively  large  and  certain  income  of  his  early  productive  years  he 
pays  for  his  insurance.  This  policy  also  appeals  to  the  man  of  middle 
age  who  has  neglected  to  purchase  life  insurance  but  who  wishes  to  buy 
it  and  pay  for  it  before  be  becomes  actually  old. 

The  Annuity 

An  annuity  is  a  specific  sum  of  money  to  be  paid  yearly  to  some 
designated  person.  The  one  to  whom  the  money  is  to  be  paid  is  termed 
the  annuitant.  If  the  payment  is  to  be  made  every  year  until  the  annui- 
tant dies,  it  is  termed  a  life  annuity.  For  example,  a  life  insurance 
company  or  other  financial  institution,  in  consideration  of  the  payment 
to  it  of  a  specified  amount,  say  §  1000,  will  enter  into  a  contract  to  pay 
a  designated  annuitant  a  stated  sum,  say  $  70,  on  a  specified  day  in  every 
year  so  long  as  the  annuitant  continues  to  live.  The  latter  may  live  to 
draw  his  annuity  for  many  years,  until  he  has  received  in  aggregate 
several  times  the  original  amount  paid  by  him,  or  he  may  die  after  having 
collected  but  a  single  payment.  In  either  case,  the  contract  expires  and 
the  annuity  terminates  with  the  death  of  the  annuitant. 

The  amount  of  the  yearly  income  or  annuity  which  can  be  purchased 
with  $  1000  will  depend,  of  course,  upon  the  age  of  the  annuitant.  That 
sum  will  buy  a  larger  income  for  the  man  of  seventy  than  for  one  of 
fifty-six,  for  the  reason  that  the  former  has,  on  the  average,  a  much 
shorter  time  yet  to  live.  The  net  cost  of  an  annuity,  that  is,  the  net 


THRIFT   AND    INVESTMENT  193 

amount  to  be  paid  in  one  sum,  and  which  is  termed  the  value  of  the 
annuity,  is  not  a  matter  of  estimate,  but,  like  the  life  insurance  premium, 
is  determined  by  mathematical  computation,  based  upon  the  mortality 
table.  The  process  is  quite  as  simple  as  the  computation  of  the  single 
premium. 

Many  men  who  insure  their  lives  choose  a  form  of  policy  under  which 
the  beneficiary,  instead  of  receiving  the  full  amount  of  the  insurance  at 
the  death  of  the  insured,  is  paid  an  annuity  for  a  period  of  years  or 
throughout  life.  The  amount  of  annuity  paid  in  such  cases  is  exactly 
equal  to  the  amount  that  could  be  bought  for  a  sum  equal  to  the  value  of 
the  policy  when  it  falls  due. 

EXAMPLES 

1.  A  young  man  at  26  years  of  age  takes  out  a  straight  life 
policy  of  $  1000,  for  which  he  pays  $  17.03  a  year  as  long  as 
he  lives,  and  his  estate  receives  $  1000  at  his  death.     If  he 
dies  at  46  years  of  age,  how  much  has  he  paid  in  ?     How  much 
more  than  he  has  paid  does  his  estate  receive  then  ? 

2.  Another  young  man  at  the  same  age  takes  out  a  twenty- 
payment  life  policy  and  pays  $  24.85  for  twenty  years.     At 
the  end  of  the  twenty  years,  how  much  has  he  paid  in  ?     Does 
he  receive  anything  in  return  at  the  end  of  the  twenty  years  ? 

3.  Another  form  of  insurance,  called  an  endowment,  is  taken 
out  by  another  young  man  at  twenty-six  years  of  age.     He 
pays  $  41.94  a  year.     At  the  end  of  twenty  years  he  receives 
$  1000  from  the  insurance  company.     How  much  has  he  paid 
in  ?     Where  is  the  difference  between  these  two  amounts  ? 

Exchange 

Exchange  is  the  process  of  making  payment  at  a  distant  place  without 
the  risk  and  expense  of  sending  money  itself.  Funds  may  be  remitted 
from  one  place  to  another  in  the  same  country  in  six  different  ways : 
Postal  money  order,  express  money  order,  telegraphic  money  order,  bank 
draft,  check,  and  sight  draft. 

The  largest  amount  for  which  one  can  obtain  a  postal  money  order  is 
$  100.  It  is  drawn  up  by  the  postmaster  after  an  application  has  been 
duly  made  out. 

An  express  money  order  is  similar  to  a  postal  money  order,  but  may  be 


194       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

drawn  for  any  number  of  dollars  at  the  same  rate  as  the  post  office  order. 
This  is  issued  at  express  offices. 

A  telegraphic  money  order  is  an  order  drawn  by  a  telegraph  agent  at 
any  office,  instructing  the  agent  at  some  other  office  to  pay  the  person 
named  in  the  message  the  sum  specified.  The  rates  are  high,  and  in 
addition  one  must  pay  the  actual  cost  of  sending  the  telegram  according 
to  distance  and  number  of  words. 

A  bank  draft  is  an  order  written  by  one  bank  directing  another  bank 
to  pay  a  specified  sum  of  money  to  a  third  party.  This  order  looks  much 
like  a  check. 

A  check  is  an  order  on  a  bank  to  pay  the  sum  named  and  deduct  the 
amount  from  the  deposit  of  the  person  who  signs  the  check. 

A  sight  draft  is  an  order  on  a  debtor  to  pay  to  a  bank  the  sum  named 
by  the  creditor  who  signs  the  draft. 

Foreign  exchange  is  a  system  for  transmitting  money  to  another  country. 
By  this  means  the  people  of  different  countries  may  pay  their  debts. 

The  most  common  methods  of  foreign  exchange  for  an  ordinary 
traveler  are  letters  of  credit  or  travelers'  cheques. 

A  letter  of  credit  is  a  circular  letter  issued  by  a  banking  house  to  a 
person  who  desires  to  travel  abroad.  The  letter  directs  certain  banks  in 
foreign  countries  to  furnish  the  traveler  such  sums  as  he  may  require  up 
to  the  amount  named  in  the  letter. 

Fees  For  Money  Orders 

Domestic  Bates 

When  payable  in  Bahamas,  Bermuda,  British  Guiana,  British  Hon- 
duras, Canada,  Canal  Zone,  Cuba,  Martinique,  Mexico,  Newfoundland, 
The  Philippine  Islands,  The  United  States  Postal  Agency  at  Shanghai 
(China),  and  certain  islands  in  the  West  Indies,  listed  in  the  register  of 
money  order  offices. 

For  Orders  from 

$00.01  to      $2.50       . Scents 

From    $  2.51  to      $  5 5  cents 

From    $  5.01  to    $  10 8  cents 

From  $  10.01  to    $  20 10  cents 

From  $  20.01  to    $  30 12  cents 

From  $  30.01  to    $  40 15  cents 

From  $  40.01  to    $  50 18  cents 

From  $  50.01  to    $  60 20  cents 

From  $  60.01  to    $75 , 25  cents 

From  $  75.01  to  $  100 ,     .     .  30  cents 


THRIFT   AND    INVESTMENT  195 

International  Rates 

When  payable  in  Asia,  Austria,  Belgium,  Bolivia,  Chile,  Costa  Rica, 
Denmark,  Egypt,  France,  Germany,  Great  Britain  and  Ireland,  Greece, 
Honduras,  Hongkong,  Hungary,  Italy,  Japan,  Liberia,  Luxemburg, 
Netherlands,  New  South  Wales,  New  Zealand,  Norway,  Peru,  Portugal, 
Queensland,  Russia,  Salvador,  South  Australia,  Sweden,  Switzerland, 
Tasmania,  Union  of  South  Africa,  Uruguay,  and  Victoria. 
For  Orders  from 

$00.01  to    $10 10  cents 

From  $  10.01  to    $  20 20  cents 

From  $  20.01  to    $  30 30  cents 

From  $  30.01  to    $  40 40  cents 

From  $  40.01  to    $  50 50  cents 

From  $50.01  to    $60 60  cents 

From  $  60.01  to    $  70 70  cents 

From  $  70.01  to    $80       . 80  cents 

From  $80.01  to    $90 90  cents 

From  $  90.01  to  $  100 1  dollar 

Rates  for  Money  Transferred  by  Telegraph 

The  Western  Union  charges  for  the  transfer  of  money  by  telegraph  to 
its  offices  in  the  United  Stales  the  following  : 

First :  For  $  25.00  or  less 25  cents 

$  25.01  to  $   50.00 35  cents 

$50.01  to  $   75.00       60  cents 

$75.01  to  $100.00 85  cents 

For  amounts  above  $  100.00  add  (to  the  $  100.00  rate)  25  cents  per  hundred 
(or  any  part  of  $  100.00)  up  to  $  3000.00. 

For  amounts  above  $  3000.00  add  (to  the  $  3000.00  rate)  20  cents  per  hundred 
(or  any  part  of  $  100.00). 

Second :  To  the  above  charges  are  to  be  added  the  tolls  for  a  fifteen  word 
message  from  the  office  of  deposit  to  the  office  of  payment. 

Express  rates  are  the  same  as  postal  rates. 

EXAMPLES 

1.  A  young  woman  in.  California  desires  to  send  $  20  to  her 
mother  in  Maine.     What  is'  the  most  economical  way  to  send 
it,  and  what  will  it  cost  ? 

2.  A  young  lady,  traveling  in  this  country,  finds  that  she 


196       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

needs  money  immediately.  What  is  the  quickest  and  most 
economical  way  for  her  to  obtain  $  275  from  her  brother  who 
lives  1000.  miles  distant  ? 

3.  A  merchant  in  Boston  buys  a  bank  draft  of  $  3480  for 
Chicago.     The  bank  charges  J   of  1  %    for  exchange.      How 
much  must  he  pay  the  bank  ? 

4.  A  domestic  in  this  country  sends  to  her  mother  in  Ireland 
5  pounds  for  a  Christmas  present.     What  will  it  cost  her,  if 
$  4.865  =  £  1  ?     A  commission  of  i  of  1  °/0  is  charged. 

Claims 

If  a  person  traveling  by  boat,  electric  or  steam  railway  is  injured  by  an 
accident  which  is  the  fault  of  the  company,  it  is  bound  to  repair  the  finan- 
cial loss.  The  company  is  not  responsible  for  the  carelessness  of  passen- 
gers or  for  the  action  of  the  elements.  When  an  accident  occurs,  the 
injured  persons  are  interviewed  by  a  claim  agent,  whom  all  large  com- 
panies employ,  and  he  offers  to  settle  with  you  for  a  certain  amount.  If 
you  are  not  satisfied  with  this  amount,  you  may  put  in  your  claim  and 
the  case  goes  to  court,  where  you  may  lose  or  win  according  to  the  decision 
of  the  jury.  When  a  wreck  occurs  on  a  railroad,  a  claim  agent  and  a 
doctor  are  brought  to  the  scene  as  soon  as  possible.  They  take  the  name 
and  address  of  each  person  in  the  accident  and  try  to  settle  the  case  at 
once,  because  it  is  expensive  to  go  to  court  and  the  newspaper  notoriety 
injures  the  reputation  of  the  company.  If  you  are  not  seriously  hurt,  the 
claim  agent  tries  to  persuade  you  to  sign  a  paper  which  relieves  the  Com- 
pany from  any  responsibility  forever  after.  For  instance,  in  a  collision 
you  seem  to  be  only  shaken  up,  not  injured.  The  claim  agent  perhaps 
offers  to  pay  you  $  25.  You  think  that  is  an  easy  way  to  get  $  25,  so  you 
take  it,  but  in  turn  you  must  sign  a  paper  which  states  that  the  company 
has  settled  in  full  with  you  for  any  claim  that  you  may  have  against  it  for 
that  accident.  Now  it  may  prove  later  that  you  have  an  internal  injury 
which  you  did  not  realize  at  the  time,  and  that  an  operation  costing  $  500 
is  necessary.  Can  you  compel  the  company  to  pay  the  bill  ?  People 
who  are  not  hurt  at  all  in  an  accident  and  to  whom  the  claim  agent  offers 
nothing  are  also  asked  to  sign  a  paper  relieving  the  company  from  all 
responsibility.  Do  not  sign  such  a  paper.  The  company  cannot  compel 
you  to,  you  gain  nothing  by  it,  and  may  lose  much  if  it  proves  later  that 
you  are  internally  injured. 


THRIFT  AND    INVESTMENT  197 

EXAMPLES 

1.  A  woman  was  riding  in  an  electric  car  that  collided  with 
another.     She  was  cut  with  flying  glass  and  was  obliged  to  hire 
a  servant  for  four  weeks  at  $8.     Doctor's  bills  amounted  to 
$24.50,  medicine,  etc.,  $8.75.     She  settled  at  the  time  of  the 
accident  for  $50.     Did  she  lose  or  gain  ? 

2.  A  man  working  in  a  mill  was  injured  in  an  elevator  acci- 
dent.    The  insurance  company  paid  his  wages  and  medical 
bills  for  8  weeks  at  $13.50  per  week.     A  year  later  he  was  out 
of  work  for  three  weeks  for  the  same  injury  and  did  not  receive 
any  compensation.     Would  it  have  been  better  for  him  to  have 
settled  for  $100  at  the  beginning? 

3.  A  saleslady  tripped  on  a  staircase  and  sprained  her  ankle. 
She  was  out  of  work  for  two  weeks  and  two  days  at  $8.75  per 
week.     Her  medical  supplies  cost  $9.75.     She  settled  for  $45. 
How  much  did  she  gain  ? 


PART   III  — DRESSMAKING   AND   MILLINERY 

CHAPTER   IX 
PROBLEMS  IN  DRESSMAKING 

THE  yardstick  is  much  used  for  measuring  cloth,  carpets, 
and  fabrics.  The  yardstick  is  divided  into  halves,  quarters, 
and  eighths.  Dressmakers  should  know  the  fractional  equiva- 
lents of  yards  in  inches  and  the  fractional  equivalents  of 
dollars  in  cents. 

It  is  wise  to  buy  to  the  nearest  eighth  of  a  yard  unless  the 
cost  per  yard  is  so  small  that  an  eighth  would  cost  as  much  as 
a  quarter. 

EXAMPLES 

1.  Give  the  equivalent  in  inches  of  the  following : 

(a)  1  yd.  (/)  4f  yd.  (fc)  1  yd. 

(b)  21  yd.  (g)  61  yd.  (/)  1  yd. 

(c)  11  yd.  (ft)  li  yd.  (m)  TV  yd. 

(d)  21  yd.  (0   1}  yd.  (n)   A  yd. 

00  3f  yd.  CO  *  yd.  00  A  yd. 

2.  A  piece  of  cloth  is  12  yd.  long.     How  many  pieces  are 
needed  for  16  aprons  requiring  11  yd.  each  ? 

3.  A  piece  of  lawn  cloth  is  28  yd.  long.     How  many  pieces 
are  needed  for  20  aprons  requiring  1|  yd.  each  ? 

4.  Give  the  value  in  cents  of  the  following  fractions  of  a 
dollar : 

(«)  if  00  it  -CO  A          «  A 

P)  i          (n  i          oo  t        «  A 

W  i  to)  I  (*)  A  (<0  i 

W  ii  W  T76  (0  A  00  t 

198 


ARITHMETIC   FOR   DRESSMAKERS  199 

5.  If  16"  is  cut  from  1|  yd.  of  cloth,  how  much  remains  ? 

6.  If  J  of  a  yard  of  lawn  is  cut  from  a  piece  40  in.  long, 
what  part  of  a  yard  is  left  ? 

7.  I  bought  9f  yd.  of  silk  for  a  dress.     If  If  yd.  remained, 
how  much  was  used  ? 

8.  A  towel  is  33  inches  long  and  and  a  dishcloth  13  inches. 

(a)  Find  the  length  of  both.     (Allow  |"  for  each  hem.) 

(b)  Find  the  number  of  yards  used  for  both. 

(c)  Find  the  number  of  inches  used  by  a  class  of  24. 

(d)  Find  the  number  of  yards  used  by  a  class  of  24. 

(e)  Find  the  cost  per  pupil  at  6  cts.  per  yard. 

(/)  Find  the  cost  for  a  class  of  24  at  6  cts.  per  yard. 

9.  If  it  took  72  yards  of  material  for  a  dishcloth  and  towel 
for  two  classes  of  24  (48  in  all),  find  the  amount  used  by  each 
pupil. 

10.  If  45f  yards  of  material  were  used  for  a  class  of  42,  find 
the  amount  used  by  each  pupil. 

11.  (a)  Reduce  75  inches  to  yards,     (b)  Find  the  number  of 
inches  in  3^-  yards,     (c)  From  2J  yards  cut  40  inches. 

Tucks 

A  tuck  is  a  fold  in  the  cloth 
for  the  purpose  of  shortening 
garments  or  for  trimming  or  dec~ 
oration.  A  tuck  takes  up  twice 
its  own  depth ;  that  is,  a  V  tuck 
takes  up  2"  of  cloth. 

EXAMPLES 

1.    Before    tucking,  a   piece   of 

goods  was  I-  yd.  long :  after  tuck- 

MEASURING  FOR  TUCKS  FROM 
ing,    it    was   |   yd.    long.      How  FoLD  T0  FOLD 

many  y  tucks  were  made  ? 


200       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

2.  How  much  lawn  is  taken  up  in  3  groups  of  tucks,  the 
first  group  containing  6  one-inch  tucks,  the  second  group  6  one- 
half-inch  tucks,  and  the  third  group  12  one-eighth-inch  tucks  ? 

3.  A  piece  of  muslin  29  inches  wide  was  tucked  and  when 
returned  to  the  teacher  was  only  14  inches  wide.     How  many 
yr  tucks  were  made  in  it  ? 

4.  Before  tucking,  a  piece  of  goods  was  f  yd.  long ;  after 
tucking,  it  was  %  yd.  long.     How  many  y  tucks  were  made  ? 


Hem 


HEM  TURNED 


A  hem  on  a  piece  of  cloth  is 
an  edge  turned  over  to  form  a 
border  or  finish.  In  making  a 
hem  an  edge  must  always  be 
turned  to  prevent  fraying ;  ex- 
cept for  very  heavy  or  very 
loosely  woven  cloth  this  is  usu- 
ally y.  For  an  inch  hem  you 
would  have  to  allow  1-". 


EXAMPLES 

1.  I  wish  to  put  three  V'  tucks  in  a  skirt- which  is  to  be  40" 
long.     How  long  must  the  skirt  be  cut  to  allow  for  the  tucks 
and  31"  hem  ? 

2.  My  cloth  for  a  ruffle  is  10"  deep.     It  is  to  have  a  1^" 
hem,  and  five  1"  tucks.     How  long  will  it  be  when  finished  ? 

3.  If. a  girl  can  hem  21  inches  in   five  minutes,  how  long 
will  she  take  to  hem  2  yards  ? 

4.  At  the  rate  of  f  of  an  inch  per  minute,  how  long  will  it 
take  a  girl  to  hem  2  yards  ?     10  yards  ? 

5.  At  the  rate  of  51  inches  per  ten  minutes,  how  long  will 
it  take  to  hem  3^  yards  ? 


ARITHMETIC    FOR   DRESSMAKERS  201 

6.  A  girl  can  hem  3  inches  in  five  minutes.     How  much  in 
an  hour  ? 

7.  How  long  will  she  take  to  hem  90  inches  ? 

8.  At  6  cents  per  hour,  how  much  can  she  earn  by  hemming 
190  inches  ? 

9.  How  long  will  it  take  a  girl  to  hem  2J  yards  if  she  can 
hem  5|  inches  in  ten  minutes  ? 

Ruffle 

A  ruffle  is  a  strip  of  cloth  gathered  in  narrow  folds  on  one 
edge  and  used  for  the  trimming  or  decoration.     Different  pro- 
portions   of    material   are   allowed 
according  to  the   use   to   which   it 
is    to    be    put.     For    the    ordinary 
ruffle    at   the    bottom    of   a    skirt, 
drawers,  apron,  etc.,  allow  once  and 
a    half.     Once    and    a    quarter    is  RUFFLE 

enough  to  allow  for  trimming  for 

a  corset  cover  or  for  other  places  where  only  a  scant  ruffle  is 
desirable.     A  plaiting  requires  three  times  the  amount. 

EXAMPLES 

1.  How  much  hamburg  would  you  buy  to  make  a  ruffle  for 
a  petticoat  which  measures  3  yd.  around,  if  once  and  a  half 
the  width  is  necessary  for  fullness  ? 

2.  How  much  lace  2^  inches  wide  would  you  buy  to  have 
plaited  for  sleeve  finish,  if  the  sleeve  measures  8  inches  around 
the  wrist  —  allowing  three  times  the  amount  for  plaiting  ? 

3.  A  skirt  measuring  3J  yd.  around  is  to  have  two  5-inch 
ruffles  of   organdie  flouncing.      Allowing  twice  the  width  of 
skirt  for   lower  ruffle,   and   once  and   three  quarters  for  the 
upper    one,  how  much   flouncing  would    you   buy,  and    what 
would  be  the  cost  at  $  .87-J  per  yard  for  organdie  ? 


202       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

4.  How   deep   must  a   ruffle   be  cut   to   be   6"  deep  when 
finished,  if  there  is  to  be  a  1-J"  hem  on  the  bottom  and  three 
i"  tucks  above  the  hem  ? 

5.  How  deep  a  ruffle  can  be  made  from  a  strip  of  lawn  16" 
deep,  if  a  2"  hem  is  on  the  bottom  and  above  it  three  \"  tucks  ? 

6.  How  many  yards  of  cloth  36"  wide 
are  needed  for  3i  yd.  of  ruffling  which  is 
to  be  cut  6"  deep? 

7.  How  many  widths  for  ruffling  can  be 
cut  from  4  yd.  of  lawn  36"  wide,  if  the 
ruffle  is   6"  finished,  and   has   a   J"  hem 

and  five  J"  tucks  ? 

NOTE.  — Allowance  must  be  made  for  joining  a  ruffle  to  a  skirt,  usu- 
ally y>. 

8.  How   deep   must  a   ruffle  be  cut  to   be  5"   deep   when 
finished,  if   there  is    to   be   a  11"   hem   on   the  bottom,  and 
five  i"  tucks  above  the  hem  ? 

9.  How  many  yards  of  ruffling  are  needed  for  a  petticoat 
21  yd.  around  the  bottom  ? 

EXAMPLES   IN   FINDING   COST  OF   MATERIALS 

1.  What  is  the  cost  of  hamburg  and  insertion  for  one  pair 

of  drawers  ? 

32  in.  around  each  leg. 
Hamburg  at  16  cents  a  yard. 
Insertion  at  15  cents  a  yard. 

2.  What  is  the  cost  of  hamburg  and  insertion  for  one  pair 

of  drawers  ? 

36  in.  around  each  leg. 
Hamburg  at  18^  cents  a  yard. 
Insertion  at  16|  cents  a  yard. 

3.  What  is  the  cost  of  hamburg  and  insertion  for  a  petticoat  ? 

5  yd.  around. 

Hamburg  at  25  cents  a  yard. 

Insertion  at  15  cents  a  yard. 


ARITHMETIC   FOR   DRESSMAKERS  203 

4.  What  is  the  cost  of  hamburg  and  insertion  for  a  petti- 
coat? 

5 1  yd.  around. 

Hamburg  at  27|  cents  a  yard. 

Insertion  at  16|  cents  a  yard. 

5.  What  is  the  cost  of  trimming  for  a  corset  cover  ? 

38  in.  around  top. 

13  in.  around  armhole. 

Lace  at  10  cents  a  yard. 

6.  What  is  the  cost  of  trimming  for  a  corset  cover  ? 

41  in.  around  top. 

13^  in.  around  armhole. 

Lace  at  12£  cents  a  yard. 

7.  What  is  the  cost  of  lace  for  neck  and  sleeves  at  121  cents 

a  yard  ? 

Neck,  13  in.,  sleeves,  8  in. 

8.  What  is  the  cost  of  lace  for  neck  and  sleeves  at  15  cents 

a  yard  ? 

Neck,  14  in.,  sleeves,  8J  in. 

9.  What  is  the  cost  of  a  petticoat  requiring  21  yd.  long- 
cloth  at  121  cents  a  yard,  and  2J  yd.  hamburg  at  151  cents 
a  yard? 

10.  What  is  the  cost  of  a  petticoat  requiring  2f  yd.  long- 
cloth  at  13  i  cents  a  yard,  and  21  yd.  hamburg  at  151  cents  a 
yard? 

11.  What  is  the  cost  of  a  nightdress  requiring  31  yd.  of 
cambric  at  25  cents   a   yard   and   3   skeins  of  D.  M.  C.   em- 
broidery cotton  which  sells  at  5  cents  for  2  skeins,  and  11  yd. 
i-inch  ribbon  at  9  cents  a  yard  ? 

12.  What  is  the  cost  of  the  following  material  for  a  corset 

cover  ? 

1£  yd.  longcloth  at  15  cents  a  yard. 
2£  yd.  hamburg  at  8  cents  a  yard. 
6  buttons  at  12    cents  a  dozen. 


204       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

13.  What  is  the  cost  of  the  following  material  for  a  skirt  ? 

7  yd.  silk  at  79  cents  a  yard. 
1-|  yd.  lining  at  35  cents  a  yard. 

14.  What  is  the  cost  of  the  following  material  for  a  corset 
cover  ? 

1$  yd.  longcloth  at  15  cents  a  yard. 
2£  yd.  hamburg  at  8^  cents  a  yard. 
4  buttons  at  12|  cents  a  dozen. 

15.  What  is  the  cost  of  the  following  material  for  a  corset 
cover  ? 

14  yd.  longcloth  at  16|  cents  a  yard. 
2f  yd.  hamburg  at  25|  cents  a  yard. 
2f  yd.  insertion  at  191  cents  a  yard. 
4  buttons  at  15  cents  a  dozen. 

16.  What  is  the  cost  of  the  following  material  for  a  corset 
cover  ? 

1|  yd.  longcloth  at  14$  cents  a  yard. 
If  yd.  hamburg  at  17$  cents  a  yard. 

17.  What  is  the  cost  of  the  following  material  for  a  skirt  ? 

7$  yd.  silk  at  83$  cents  a  yard. 
1$  yd.  lining  at  37$  cents  a  yard. 

18.  Find  the  cost  of  a  corset  cover  that  requires 

1  yd.  cambric  at  12$  cents  a  yard, 
f  yd.  bias  binding  at  2  cents  a  yard, 
i  doz.  buttons  at  12  cents  a  dozen. 
If  yd.  lace  at  10  cents  a  yard. 
\  spool  thread  at  5  cents  a  spool. 

19.  Find  the  cost  of  an  apron  that  requires 

1  yd.  lawn  at  12$  cents  a  yard. 
2^  yd.  lace  at  10  cents  a  yard. 
\  spool  thread  at  5  cents  a  spool. 


ARITHMETIC   FOR   DRESSMAKERS  205 

20.  Find  the  cost  of  a  nightgown  containing 

3|  yd.  cambric  at  12|  cents  a  yard. 

2  yd.  lace  at  5  cents  a  yard. 

3  yd.  ribbon  at  3  cents  a  yard. 

\  spool  thread  at  5  cents  a  spool. 

21.  Find  the  cost  of  drawers  containing 

2  yd.  cambric  at  12|  cents  a  yard. 
1^  yd.  finishing  braid  at  5  cents  a  yard. 
\  spool  thread  at  5  cents  a  spool. 
2  buttons  at  10  cents  a  dozen. 

22.  What  is  the  cost  of  a  waist  made  of  the  following  ? 

2f  yd.  shirting,  32  inches  wide,  at  23  cents  a  yard. 
Sewing  cotton,  buttons,  and  pattern,  25  cents. 

23.  What  is  the  cost  of  1\  yd.  chiffon  faille,  36  inches  wide, 
at  $  1.49  a  yard  ? 

24.  How  many  yards  of  ruffling  are  needed  for  1  dozen  aprons 
if  each  apron  is  one  yard  wide  and  half  the  width  of  the  apron 
is  added  for  fullness  ? 

25.  How  many  pieces  of  lawn-36  inches  wide  are  needed  for 
the  ruffle  for  one  apron  ?     For  eight  aprons  ? 

26.  A  skirt  measures  2|  yards  around  the  bottom.     How 
much  material  is  needed  for  ruffling  if  the  material  is  one  yard 
wide  and  ruffle  is  to  be  cut  7  inches  wide  ? 

27.  How  deep  would  you  cut  a  cambric  ruffle  that  when 
finished  will  measure  121",  including  the  hamburg  edge  which 
measures  4",  two  clusters  of  5  tucks  -J-"  deep,  and  allowing  V 
for  making  ? 

28.  Find  the  cost  of  a  poplin  suit  made  of  the  following  : 

Silk  poplin,  40  inches  wide  :  5|  yards,  at  $  1.79  a  yard. 
Satin  facing  for  collar,  revers,  and  cuffs,  21  inches  wide  :  1  yard,  at 
$1.25  a  yard. 

Coat  lining,  36  inches  wide  :  2f  yards,  at  $  1.50  a  yard. 
Buttons,  braid,  sewing  silk,  two  patterns,  $  .64. 


206       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


Cloths  of  Different  Widths 

There  are  in  common  use  cloths  of  several  different  widths 
and  at  various  prices.  It  is  often  important  to  know  which  is 
the  most  economical  cloth  to  buy.  This  may  be  calculated  by 
finding  the  cost  per  square  yard,  36"  by  36".  To  illustrate : 
which  is  less  expensive,  broadcloth  56"  wide,  at  $2.25  per 
yard,  or  50"  wide,  at  $1.75  per  yard  ? 

36  x  ^  x  2.25  =  $  1.44&  per  square  yard. 
56  x  3^ 

36  x  W  x  1.75  =  $  1.26  per  square  yard. 


EXAMPLES 

Find  the  cost  per  square  yard  and  the  relative  economy  in 
purchasing  : 

(a)  Prunella,  46"  wide,  at  $  1.50  a  yard. 
Prunella,  44"  wide,  at  $  1.35  a  yard. 

(6)  Serge,  54"  wide,  at  $  1.25  a  yard. 
Poplin,  42"  wide,  at  $  1.00  a  yard. 

(c)  Serge,  42"  wide,  at  49  cents  a  yard. 
Serge,  37"  wide,  at  39  cents  a  yard. 

(<Z)  Shepherd  check,  54"  wide,  at  $  1.75  a  yard. 
Shepherd  check,  52"  wide,  at  $  1.50  a  yard. 
Shepherd  check,  42"  wide,  at  $  1.00  a  yard. 

(e)  Taffeta,  19"  wide,  at  89  cents  a  yard. 
Taffeta,  36"  wide,  at  $  1.25  a  yard. 

(/)  Cashmere,  42"  wide,  at  $  1.00  a  yard. 
Nuns  veiling  44"  wide,  at  75  cents  a  yard. 

($r)  Cheviot,  57"  wide,  at  $1.50  a  yard. 
Diagonal,  54"  wide,  at  $2.00  a  yard. 

(A)  Messaline,  26  "  wide,  at  59  cents  a  yard. 
Messaline,  36  "  wide,  at  $  1.25  a  yard. 


ARITHMETIC   FOR   DRESSMAKERS  207 

PROBLEMS   IN   TRADE   DISCOUNT 

ILLUSTRATIVE  EXAMPLE.  —  A  dressmaker  bought  $  125  worth 
of  material,  receiving  6  %  discount  for  cash.  She  sold  the 
material  for  20  %  more  than  the  original  price.  What  was  the 
gain? 

SOLUTION.  —  $  125.00  original  price      $125.00 
.06  7.50 

$  7.50  discount  $  117.50  price  paid  for  material. 

5[$125  original  cost  $  150.00  selling  price 

$25  20  %  gain  117.50  price  paid 

$  150  selling  price  $32. 50  gain.     Am. 

EXAMPLES 

1.  A  dressmaker  bought  25  yd.  of  hamburg  at  50  cents  per 
yard,  receiving  6  %  discount  for  cash.     She  then  sold  the  ham- 
burg  to  her  customers  at  60  cents  per  yard.     What  was  the 
price  paid  for  hamburg,  and  what  per  cent  did  she  make  ? 

2.  A  dressmaker  bought  $  325  worth  of  goods,  receiving  6  °/0 
discount  for  cash.     She  sold  the  goods  for  25  %  more  than  the 
original  price.     What  was  the  gain  ? 

3.  A  milliner  bought  $200  worth  of  ribbons,  velvets,  and 
flowers,  receiving  5  %  discount  for  cash.     She  then  sold  the 
materials  for  30  %  more  than  the  original  price.     What  was 
the  gain  ? 

REVIEW  EXAMPLES 

1.  A  dressmaker  bought  30  yd.  of  silk  at  $  1.25  per  yard. 
She  received  a  discount  of  10  %.     She  sold  the  silk  for  $  1.39 
per  yard.     How  much  did  she  gain  on  the  30  yards  ? 

2.  A  merchant  bought  50  yd.  of  lawn  at  12^  cents  a  yard, 
and  received  a  discount  of  6  %  for  cash.     How  much  did  the 
lawn  cost  ? 

3.  A  piece  of  crinoline  containing  45  yd.  was  bought  for 
$  18.    It  was  made  into  dress  models  of  5  yd.  each.     What  was 
the  cost  of  the  crinoline  in  each  model  ? 


208       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

4.  A   dressmaker  bought  $  175  worth  of  silk,  receiving  6  % 
discount  for  cash.     She  sold  the  silk  for  25  %  more  than  the 
original  price.     What  was  the  gain  per  cent  ? 

5.  A  dressmaker  bought  24J  yd.  of  silk,  at  $  1.10  per  yard. 
From  it  she  made  three  dresses,  and  had  13f  yd.  left.     How 
much  did  the  silk  for  one  dress  cost  ? 

6.  Find  the  cost  of  ,36  yd.  of  Valenciennes  lace  at  7^  cents 
a  yard,  12  yd.  of  insertion  at  6|-  cents  a  yard,  and  12  yd.  of 
beading  at  7  cents  a  yard.     What  is  the  net  cost,  when  2  % 
discount  is  given  ? 

7.  How  many  lingerie  shirtwaists,  each  containing  2|  yd., 
can  be  made  from  49  yd,  of  batiste  ?     What  is  the  cost  of 
material  for  one  waist,  if  the  whole  piece  cost  $  9.80,  less  5  % 
discount  ? 

8.  A  dressmaker  bought  2i  yd.  of  crepe  at  29  cents  a  yard, 
for  a  shirtwaist,  3  yd.  of  beading  at  121  cents  a  yard,  6  crochet 
buttons  at  35  cents  a  dozen.     What  did  the  material  for  the 
waist  cost  ? 

9.  A  woman  bought  91  yd.  of  foulard  silk,  at  $  1.10  a  yard, 
for  a  dress,  If  yd,  of  net  at  $  1.50  a  yard,  and  J  yd.  of  plain 
silk  at  $  1.25  a  yard.     What  was  the  cost  of  material  ? 

10.  A  dressmaker  bought  50  yd,  of  taffeta  silk  for  $  45.00. 
She  sold  81  yd.  to  one  customer  for  $  1.25  a  yard,  151  yd.  at 
$  1.00  a  yard  to  another  customer,  and  the  remainder  at  cost. 
What  did  she  gain  on  the  entire  piece  ?     What  was  the  gain 
per  cent  ? 

11.  Two  and  one-half  yards  of  cloth  cost  $  2.75.     What  was 
the  price  per  yard  ? 

12.  A  dressmaker  bought  50  yd.  of  handmade  lace  abroad 
and  paid  $  75  for  it.     She  paid  60  %  duty  on  the  lace  and  sold 
it  at  a  gain  of  33^  %  •     What  was  the  selling  price  per  yard  ? 


ARITHMETIC   FOR   DRESSMAKERS  209 

13.  A  dressmaker  bought  20  yd.  of  foulard  silk  at  90  cents 
a  yard.     She  received  6  %   discount.     She  sold  it  for  10£  % 
more  than  the  original  price.     How  much  did  she  gain  on  the 
sale  ?     What  per  cent  did  she  gain  ? 

14.  A   dressmaker   bought   the    following   materials   for   a 
customer :  4^  yd.  of  broadcloth  at  $  2.75  a  yard,  6-J-  yd.  of  silk 
at  $3.75  a  yard,  2-^  yd.  of  trimming  at  $2.50  a  yard.     She 
received  a  dressmaker's  discount  of  6  % ,  and  5  %  discount  for 
cash  payment.     What  did  she  pay  for  the  materials?     She 
charged  the  retail  price  for  them.     How  much  did  she  gain  ? 
What  per  cent  ? 

15.  A  dressmaker  bought  a  7^-yd.  remnant  of  broadcloth 
for  $  22.50.     She  sold  6  yd.  to  a  customer  at  $  3.50  a  yard,  but 
the  remainder  could  not  be  sold.     Did  she  gain  or  lose  ?     What 
per  cent  ? 

16.  A  dressmaker  bought  in  France  three  15-yd.  pieces  of 
dress   silk   at  25^  cents  a  yard.      After   paying   60  %   duty 
on  them,  she  sold  two  pieces  to  one  customer  at  48  %  gain,  and 
the  third  piece  to  another  customer  at  35  %  gain.     What  was 
the  gain  on  the  three  pieces  ? 

•  17.  A  dressmaker  furnished  the  materials  for  a  lingerie 
dress  and  charged  $25  for  it.  For  the  materials  she  paid 
the  following :  10  yd.  of  dimity  at  45  cents  a  yard,  12i  yd. 
Cluny  insertion  at  25  cents  a  yard,  findings,  $2.  If  she 
charged  $12  for  making,  how  much  did  she  gain  on  the 
material  ?  Make  a  bill  for  the  same  and  receipt  it. 

18.  The  materials  for  a  dress   cost  a  dressmaker  $  14.50. 
She  sold  them  for  10%  more  than  cost  and  charged  $15  for 
making.     She  paid  her  helper  20  %  of  the  amount  received. 
What  was  the  gain  f>er  cent  ? 

19.  If  it  takes  6^  yards  of  cloth  52  inches  wide  to  make 
a  dress,  how  many   yards  of   cloth   22   inches  wide  will   be 
needed  to  make  the  same  dress  ? 


210       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

20.  A  dressmaker  agreed  to  make  a  dress  for  a  customer  for 
$  25.     She  paid  2  assistants   $  1.25  a  day  each  for  31  days 
of  work.     The   dress  was   returned   for  alterations,   and  the 
assistants  were  paid  for  one  more  day's  work.     How  much  did 
the  dressmaker  receive  for  her  own  work  ? 

21.  A  dressmaker   bought    $1.50  worth   of   silk,  receiving 
6  %  discount  for  cash.     She  sold  the  silk  for  40  %  more  than 
the  original  price.     What  was  the  gain  per  cent  ? 

22.  A  dressmaker  has  an  order  for  three  summer  dresses, 
for  which  31 J  yd.  of  batiste  are  needed.     She  can  buy  three 
remnants  of  101  yd.  each  for  25  cents  a  yard,  or  she  can  buy  a 
piece  of  35  yd.  for  25  cents  a  yard  and  receive  4  %  discount 
for  cash.     Which  is  the  better  plan  ? 

23.  (a)  How  many  inches  in  f  yd.  ?  (b)  How  many  inches 
in  I  yd.  ?   (c)  How  many  inches   in  f  yd.  ?  (d)   How  many 
inches  in  J  yd.  ?   (e)  How  many  inches  in  -J  yd.  ?   (/)  How 
many  inches  in  J  yd.  ?  (g)  How  many  inches  in  |-  yd.  ? 

24.  Find  the  cost  of  each  of  the  above  lengths  in  lace  at 
$  .121  a  yard. 

25.  Find  the  cost  of  4^  yd.  of  lace  at  $1.95  per  piece  (one 
piece  =  12  yd.). 

26.  A  dressmaker  bought  2  pieces  of  white  lining  taffeta, 
one  piece  42  yd.  and  another  48 J  yd.,  at  $  .421  a  yard.     What 
was  the  total  cost  ? 

27.  A  piece  of  crinoline  containing  421  yd.  that  cost  $  1.70 
a  yard  was   made  into  dress  models  of   81  yd.  each.     What 
was  the  cost  of  the  crinoline  in  each  model  ? 

28.  What  is  the  cost  of  a  child's  petticoat  containing : 

2J  yd.  longcloth  at  15  cents  a  yard, 
If  yd.  hamburg  at  19  cents  a  yard, 
1£  yd.  insertion  at  15  cents  a  yard  ? 


ARITHMETIC    FOR   DRESSMAKERS  211 

29.  What  is  the  cost  of  two  petticoats  requiring  for  one : 

2£  yd.  longcloth  at  19  cents  a  yard, 
3  yd.  hamburg  at  25  cents  a  yard, 
2£  yd.  insertion  at  19  cents  a  yard  ? 

30.  What  is  the  cost  of  a  petticoat  requiring : 

3  yd.  longcloth  at  12£  cents  a  yard, 
3£  yd.  hamburg  at  17  cents  a  yard  ? 

31.  What  is  the  total  cost  of  the  following  ? 

Wedding  gloves,  $  2.75. 

Slippers  and  stockings,  $5.00. 

Six  undervests,  at  19  cents  each. 

Six  pairs  of  stockings,  at  33£  cents  a  pair. 

Two  pairs  of  shoes,  at  $  5.00  a  pair. 

One  pair  of  rubbers,  75  cents. 

One  pair  long  silk  gloves,  §2.00. 

One  pair  of  long  lisle  gloves,  $  1.00. 

Two  pairs  of  short  silk  gloves,  $  1.00. 

Veils  and  handkerchiefs,  $5.00. 

Two  hats,  $  10.00. 

Corsets,  $3.00. 

Wedding  veil  of  3  yards  of  tulle,  2  yards  wide,  at  89  cents  a  yard. 

32.  What  is  the  cost  of   the  following  material  for  a  top 
coat? 

Cotton  corduroy,  32  inches  wide  :  4|  yards  at  75  cents  a  yard. 
Lining,  36  inches  wide  :  4]  yards  at  $  1.50  a  yard. 
Buttons,  sewing  silk,  pattern,  27  cents. 
Velvet  for  collar  facing,  J  yard,  at  $1.50  a  yard. 

33.  What  is  the  cost  of  the  following  dressmaking  supplies  ? 

|  yard  of  China  silk,  27  inches  wide,  at  49  cents  a  yard  (for  the  lining). 

If  yard  of  mousseline  de  soie  interlining  40  inches  wide,  at  80  cents 
a  yard. 

f  yard  of  all-over  lace  36  inches  wide,  at  $1.48  for  front  and  lower 
back. 

\  yard  of  organdie  at  $1.00,  32  or  more  inches  wide,  for  collar  and  vest. 

Sewing  silk,  hooks  and  eyes,  pattern,  at  32  cents. 


212       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

34.  What  is  the  cost  of  the  following  ? 

Cotton  gabardine,  36  inches  wide  :  5f  yards  at  39  cents  a  yard. 
Sewing  cotton,  braid,  buttons,  pattern,  at  35  cents. 

35.  Which  of  the  following  fabrics  is  the  most  economical 

to  buy  ? 

Crepe  meteor,  44"  wide,  at  $3.25  a  yard. 
Faille  Franchise,  42"  wide,  at  $3.00. 
Charmeuse,  40"  wide,  at  $2.25. 
Louisine,  38"  wide,  at  $2.00. 
Armure,  20"  wide,  at  $1.50. 
Satin  duchesse,  21"  wide,  at  $1.25. 

MILLINERY  PROBLEMS 

1.  What  would  a  hat  cost  with  the  following  trimmings  ? 

1|  yd.  velvet,  at  $2.50  a  yard. 

£  yd.  satin  for  facing,  at  $  1.98  a  yard. 

2  feathers,  at  $  5.50  each. 

Frame  and  work,  at  $2.50. 

Make  out  a  bill.     (See  lesson  on  Invoice,  Chapter  XI,  page 
243.) 

2.  A  leghorn  hat   cost  $6.98.     Four  bunches  of  fadeless 
roses  at  $2.98,  2  bunches  of  foliage  at  $.98,  and  11  yd.  of 
velvet  ribbon  at  $  1.49  were  used  for  trimming.     The  milliner 
charged  75  cents  for  her  work.     How  much  did  the  hat  cost  ?• 

3.  A   milliner  used  the  following  trimmings  on  a  child's 

bonnet : 

1  piece  straw  braid,  at  $1.49. 

2  yd.  maline,  at  25  cents  a  yard. 

4  bunches  flowers,  at  69  cents  each. 
4  bunches  foliage,  at  49  cents  each. 
Work,  at  $2.00. 

What  was  the  total  cost  of  the  hat  ?     Make  out  a  bill  and 
receipt  it. 


ARITHMETIC   FOR   MILLINERS  213 

4.  An  old  lady's  bonnet  was  trimmed  with  tlie  following : 

3  yd.  silk,  at  $  1.50  a  yard. 

1  piece  of  jet,  83.00. 

2  small  aigrettes,  at  $  1.50  each. 
Ties,  75  cents. 

Work,  $  1.50. 

How  much  did  the  finished  bonnet  cost  ? 

5.  What  was  the  total  cost  of  a  hat  with  the  following  trim- 
mings ? 

2  pieces  straw  braid,  at  §2.50  each. 

2  yd.  velvet  ribbon,  at  98  cents  a  yard. 
5  flowers,  at  59  cents. 

4  foliage,  at  49  cents. 
Frame  and  work,  at  $2.50. 

6.  A   milliner   charged   $  2.00   for  renovating  an   old   hat. 
She  used  2  yd.  satin  at  $  1.50  a  yard  and  charged  $  2.25  for 
an  ornament.  .  How  much  did  the  hat  cost  ? 

7.  The  following  trimmings  were  used  on  a  child's  hat : 

3  yd.  velvet,  at  8  1.50  a  yard. 
8  yd.  lace,  at  15  cents  a  yard. 

2  bunches  buds,  at  49  cents  a  bunch. 
Work,  §2.00. 

How  much  did  the  hat  cost  ? 

8.  A  milliner  charged  $  6.00  for  renovating  three  feathers, 
$  2.50  for  a  fancy  band,  $  4.75  for  a  hat,  and  75  cents  for 
work.     How  much  did  the  customer  pay  for  her  hat  ? 

9.  A  lady  bought  a  hat  with  the  following  trimmings : 

2  yd.  satin,  at  $  1.75  a  yard. 
2  bunches  grapes,  at  $  1.59  a  bunch. 
2|  yd.  ribbon,  at  69  cents  a  yard. 
Work,  75  cents. 

How  much  did  the  hat  cost  ? 


214       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

10.  What  would  a  hat  cost  with  the  following  trimmings  ? 

2  pieces  straw  braid,  at  $  1.98  each. 

3  yd.  ribbon,  at  89  cents  a  yard. 
Fancy  feather,  $6.98. 

Frame  and  work,  $  2. 50. 

11.  Estimate  the  cost  of  a  hat  using  the  following  materials  : 

2£  yd.  plush,  at  $2.25  a  yard. 
2  yd.  ribbon,  at  25  cents  a  yard, 
f  yd.  buckram,  at  25  cents  a  yard. 
^  yd.  tarlatan,  at  10  cents  a  yard. 
1  band  fur,  75  cents. 
Foliage,  10  cents. 
Labor,  $2.00. 

12.  If  the  true  bias  from  selvedge  to  selvedge  is  about  ^ 
longer  than  the  width  of  the  goods,  how  many  bias  strips  must 
be  cut  from  velvet  18"  wide  in  order  to  have  a  three-yard  bias 
strip  ? 

13.  The  edge  of  a  hat  measures 
45  inches  in  circumference ;  the 
velvet  is  16  inches  wide.  How 
many  bias  strips  of  velvet  would 
it  take  to  fit  the  brim  ? 
WIRE  HAT  FRAME  ^  what  amount  of  velyet  wou]d 

be  needed  to  cover  brim  if  each  strip  cut  measured  f  of  a  yard 
along  the  selvedge  ? 

15.  Give  the  number  of  13^-in.  strips  that  can  be  cut  from 
3|-  yards  of  material ;  also  the  number  of  inches  of  waste. 

16.  How  many  22^-in.    strips   can  be  cut   from   2J  yd.  of 
material  ? 

17.  What  length  bias  strip  can  be  made  from  11  yd.  of  silk, 
each  strip  1  yd.  10  in.  long  and  1^  in.  wide? 

18.  How  many  six-petal  roses  can  be  made  from  1  yard  of 
velvet  18  inches  wide,  each  petal  cut  3  inches  square  ? 


ARITHMETIC   FOR   MILLINERS  215 

19.  Estimate  the  total  cost  of  roses,  if  velvet  is  $  1.50  a 
yard,  centers  18  cents  a  dozen,  sprays  12  cents  a  dozen,  stem- 
ming 6  cents  a  yard,  using  1  of  a  yard  for  each  flower. 

20.  Find  the  cost  of  one  flower ;  the  cost  of  ^  of  a  dozen 
flowers,  using  the  figures  given  above. 

21.  What  amount  of  velvet  will  be  needed  to  fit  a  plain-top 
facing  and  crown  of  hat,  width  of  brim  5  inches,  diameter  of 
headsize  7£  inches,  diameter  of  crown  151  inches,  allowing  81 
inches  on  brim  for  turning  over  edges  ? 

22.  If  the  circumference  of  the  brim  measures  56  inches, 
what  amount  of  silk  will  it  take  for  a  shirred  facing  made  of 
silk  22  inches  wide,  allowing  twice  around  the  hat  for  fullness, 
and  also  allowing  1  inch  oil  depth  of  silk  for  casings  ? 

23.  At  the  wholesale  rate  of  eight  frames  for  one  dollar, 
what  is  the  cost  of  five  dozen  frames  ?  of  twelve  dozen  ? 

24.  A  milliner  had  2J  dozen  buckram  frames  at  $  3.60  a 
dozen.     She  sold  |-  of  them  at  75  cents  each,  but  the  others 
were  not  sold.     Did  she  gain  or  lose  and  what  per  cent  ? 

25.  Flowers  that  were  bought  at   $  5.50  a  dozen  bunches 
were  sold  at  75  cents  a  bunch.     What  was  the  gain  on  11 
dozen  bunches  ? 

26.  A  milliner  bought  ten  rolls  of  ribbon,  ten  yards  to  the 
roll,  for  $  8.50.     Ten  per  cent  of  the  ribbon  was  not  salable. 
The  remainder  was  sold  at  19  cents  a  yard.     How  much  was 
the  gain  ?  what  per  cent  ? 

27.  A  piece  of  velvet  containing  twelve  yards  was  bought 
for   $28.20  and  sold  for   $2.75  per   yard.     How  much  was 
gained  on  the  piece  ? 

28.  A  thirty-six  yard  piece  of  maline  cost  $  7.02  and  was 
sold  at  29  cents  a  yard.     One  yard  was  lost  in  cutting.     How 
much  was  gained  on  the  piece  ? 


216       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

29.  Find  cost  of  a  velvet  hat  requiring 

1|  yd.  of  velvet,  at  $  1.50  a  yard. 
|  yd.  of  fur  band,  at  34.00  a  yard. 
1  feather  ornament,  at  $  3.00. 
Hat  frame,  50  cents. 
Edge  wire,  10  cents. 
Taffeta  lining,  25  cents. 
Making,  $  2.50. 

30.  A  milliner  charged  $  8.37  for  a  hat.     She  paid  37  cents 
for  the  frame,  $  2.80  for  the  trimming,  and  $  1.50  for  labor. 
What  was  the  per  cent  profit  ? 

31.  A  child's  hat  of  organdie  has  two  ruffles  edged  with 
Valenciennes  lace.    The  lower  ruffle  is  3"  wide  ;  the  upper  ruffle, 

2i-".  2J  yd.  lace  edging  cost  12^  cents  a  yard, 
2  yd.  of  3"  ribbon  cost  25  cents  a  yard,  11  yd. 
of  organdie  cost  25  cents  a  yard,  the  hat  frame 
cost  35  cents,  and  the  lining  cost  10  cents. 
Find  the  total  cost. 

32.  How  much  velvet  at  $  2.00  a  yard  would  you  buy  to 
put  a  snap  binding  on  a  hat  that  measures  43"  around  the 
edge  ?     Should  the  velvet  be  bias  or  straight  ? 


CHAPTER   X 
CLOTHING 

SINCE  about  one  aighth  of  the  income  in  the  average  working- 
man's  family  is  spent  for  clothing,  this  is  a  very  important 
subject.  The  housewife  purchases  the  linen  for  the  house  and 
her  own  wearing  apparel.  It  is  not  uncommon  for  her  to  have 
considerable  to  say  about  the  clothing  of  the  men,  particularly 
about  the  underclothing.  Therefore  she  should  know  some- 
thing about  what  constitutes  a  good  piece  of  cloth,  and  be  able 
to  make  an  intelligent  selection  of  the  best  and  most  economical 
fabric  for  a  particular  purpose.  The  cheapest  is  not  always 
the  best,  although  it  is  in  some  cases. 

All  kinds  of  cloth  are  made  by  the  interlacing  (weaving)  of 
the  sets  of  thread  (called  yarn).  The  thread  running  length- 
wise is  the  strongest  and  is  called  the  warp.  The  other  thread 
is  called  the  filling.  Such  fabrics  as  knitted  materials  and  lace 
are  made  by  the  interlacing  of  a  single  thread.  Threads 
(yarn)  are  made  by  lengthening  and  twisting  (called  spinning) 
short  fibers.  Since  the  fibers  vary  in  such  qualities  as  firmness, 
length,  curl,  and  softness,  the  resulting  cloth  varies  in  the 
same  way.  This  is  the  reason  why  we  have  high-grade,  medium- 
grade,  and  low-grade  fabrics. 

The  principal  fabrics  are  wool,  silk,  mohair,  cotton,  and  flax 
(linen). 

The  consumer  is  often  tempted  to  buy  the  cheaper  fabrics 
and  wonders  why  there  is  such  a  difference  in  price.  This 
difference  is  due  in  part  to  the  cost  of  raw  material  and  in  part 
to  the  care  in  manufacturing.  For  example,  raw  silk  costs 
from  $  1.35  to  $  5.00  a  pound,  according  to  the  nature  and 

217 


218        VOCATIONAL   MATHEMATICS   FOR   GIRLS 

quality  of  the  silk.  The  cost  of  preparing  the  raw  silk  aver- 
ages about  55  cents  a  pound,  according  to  the  nature  of  the 
twist,  which  is  regulated  by  the  kind  of  cloth  into  which  it  is 
to  enter.  The  cost  of  dyeing  varies  from  55  cents  to  $  1.50  a 
pound.  Weavers  are  paid  from  2  to  60  cents  a  yard  for  weav- 
ing, the  price  varying  according  to  the  desirability  of  the  cloth. 
When  we  compare  the  relative  values  of  similar  goods 
produced  by  different  manufacturers,  there  are  a  few  general 
principles  by  which  good  construction  can  easily  be  determined. 
The  density  of  a  fabric  is  determined  by  the  number  of  warp 
yarn  and  filling  yarn  to  the  inch.  This  is  usually  determined 
by  means  of  a  magnifying  glass  with  a  \"  opening.  To  illus- 
trate :  If  there  are  36  threads  in  the  filling  and  42  threads  in 
the  warp  to  J",  what  is  the  density  of  the  cloth  to  the  inch  ? 

SOLUTION.  — 

36  x  4  =  144  threads  in  the  filling. 
42  x  4  =  168  threads  in  the  warp. 

EXAMPLES 

1.  A  25-cent  summer  undervest  (knitted  fabric)  will  outwear 
two  of  the  flimsy  15-cent  variety  in  addition  to  retaining  better 
shape.     What  is  the  gain,  in  wear,  over  the  15-cent  variety  ? 

2.  A  50-cent  undervest  will  outwear  three  of  the  25-cent 
variety.     What  is  gained  by  purchasing  the  50-cent  style  ? 

3.  A  cotton  dress  for  young  girls,  costing  75  cents  ready 
made,  will  last  one  season.     A  similar  dress  of  better  material 
costs  94  cents,  but  will  last  two  seasons.     Why  is  the  latter 
the  better  dress  to  buy  ?     What  is  gained  ? 

4.  A  linen  tablecloth  (not  full  bleached)   costing  $1.04  a 
yard,  will  last  twice  as  long  as  a  bleached  linen  at  $  1.25  a 
yard.     Which  is  the  better  investment  ? 

5.  A  sheer  stocking  at  50  cents  will  wear  just  half  as  long 
as  a  thicker  stocking  at  35  cents.     What  is  gained  in  wear  ? 
What  kind  of  stockings  should  be  selected  for  wear  ? 


CLOTHING  219 

SHOES 

Our  grandfathers  and  grandmothers  wore  handmade  shoes, 
and  wore  them  until  they  had  passed  their  period  of  usefulness. 
At  that  time  the  consumption  of  leather  did  not  equal  its  pro- 
duction. But,  since  the  appearance  of  machine-made  shoes, 
different  styles  are  placed  on  the  market  at  different  seasons 
to  correspond  to  the  change  in  the  style  of  clothing,  and  are 
often  discarded  before  they  are  worn  out.  Thus  far  we  have 
not  been  able  to  utilize  cast-off  leather  as  the  shoddy  mill  uses 
cast-off  wool  and  silk.  The  result  is  that  the  demand  for 
leather  is  above  the  production  ;  therefore,  as  in  the  case  of 
textiles,  substitutes  must  be  used.  In  shoe  materials  there  is 
at  present  an  astonishing  diversity  and  variety  of  leather  and 
its  substitutes.  Every  known  leather  from  kid  to  cowhide  is 
used,  and  such  textile  fabrics  as  satins,  velvets,  and  serges 
have  rapidly  grown  in  favor,  especially  in  the  making  of 
women's  and  children's  shoes.  Of  course,  we  must  bear  in 
mind  that  for  wearing  qualities  there  is  nothing  equal  to 
leather.  In  buying  a  pair  of  shoes  we  should  try  to  combine 
both  wearing  qualities  and  simple  style  as  far  as  possible. 

EXAMPLE 

1.  A  pair  of  shoes  at  $  1.75  was  purchased  for  a  boy.  The 
shoes  required  80  cents  worth  of  mending  in  two  months.  If 
a  $3.00  pair  were  purchased,  they  would  last  three  times  as 
long  with  95  cents  worth  of  mending.  How  much  is  gained 
by  purchasing  a  $  3.00  pair  of  shoes  ? 

YARNS 

Worsted  Yarns.  — All  kinds  of  yarns  used  in  the  manufacture 
of  cloth  are  divided  into  sizes  which  are  based  on  the  relation 
between  weight  and  length.  To  illustrate  :  Worsted  yarns  are 
made  from  combed  wools,  and  the  size,  technically  called  the 


220       VOCATIONAL   MATHEMATICS   FOR   GIRLS 


counts,  is  based  upon  the  number  of  lengths  (called  hanks)  of 
560  yards  required  to  weigh  one  pound. 


ROVING  OR  YARN  SCALES 

These  scales  will  weigh  one  pound  by  tenths  of  grains  or  one  seventy-thou- 
sandth part  of  one  pound  avoirdupois,  rendering  them  well  adapted  for  use 
in  connection  with  yarn  reels,  for  the  numbering  of  yarn  from  the  weight 
of  hank,  giving  the  weight  in  tenths  of  grains  to  compare  with  tables. 

Thus,  if  one  hank  weighs  one  pound,  the  yarn  will  be  number  one 
counts,  while  if  20  hanks  are  required  for  one  pound,  the  yarn  is  the  20's, 
etc.  The  greater  the  number  of  hanks  necessary  to  weigh  one  pound,  the 
higher  the  counts  and  the  finer  the  yarn.  The  hank,  or  560  yards,  is  the 
unit  of  measurement  for  all  worsted  yarns. 

LENGTH  FOR  WORSTED  YARNS 


No. 

YARDS 
PER  LH. 

No. 

YARDS 
PER  Lu. 

No. 

YARDS 
PER  LB. 

No. 

YARDS 
PER  LB. 

1 

560 

5 

2800 

9 

5040 

13 

7280 

2 

1120 

6 

3360 

10 

5600 

14 

7840 

3 

1680 

7 

3920 

11 

6160 

15 

8400 

4 

2240 

8 

4480 

12 

6720 

16 

8960 

Woolen  Yarns.  —  In  worsted  yarns  the  fibers  lie  parallel  to 
each  other,  while  in  woolen  yarns  the  fibers  are  entangled. 


CLOTHING 


221 


This  difference  is  due  entirely  to  the  different  methods  used 
in  working  up  the  raw  stock. 

In  woolen  yarns  there  is  a  great  diversity  of  systems  of  grading,  vary- 
ing according  to  the  districts  in  which  the  grading  is  done.  Among  the 
many  systems  are  the  English  skein,  which  differs  in  various  parts  of  Eng- 
land ;  the  Scotch  spyndle  ;  the  American  run ;  the  Philadelphia  cut ;  and 
others.  In  these  lessons  the  run  system  will  be  used  unless  otherwise 
stated.  This  is  the  system  used  in  New  England.  The  run  is  based  upon 
100  yards  per  ounce,  or  1600  yards  to  the  pound.  Thus,  if  100  yards  of 
woolen  yarn  weigh  one  ounce,  or  if  1600  yards  weigh  one  pound,  it  is 
technically  termed  a  No.  1  run ;  and  if  300  yards  weigh  one  ounce,  or  4800 
yards  weigh  one  pound,  the  size  will  be  No.  3  run.  The  finer  the  yarn, 
or  the  greater  the  number  of  yards  necessary  to  weigh  one  pound,  the 
higher  the  run. 


YARN  REEL 
For  reeling  and  measuring  lengths  of  cotton,  woolen,  and  worsted  yarns. 

LENGTH  FOR  WOOLEN  YARNS  (RUN  SYSTEM) 


No. 

YARDS 

PER  1,1$. 

No. 

YARDS 
PER  LB. 

No. 

YARDS 
PER  LB. 

No. 

YARDS 
PER  LB. 

i 

200 

1 

1600 

2 

3200 

3 

4800 

* 

400 

u 

2000 

2* 

3600 

8* 

5200 

\ 

800 

11 

2400 

2^ 

4000 

3| 

5600 

1 

1200 

if 

2800 

2f 

4400 

222       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

Raw  Silk  Yarns.  —  For  raw  silk  yarns  the  table  of  weights 
is: 

16  drams  =  1  ounce 

16  ounces  =  1  pound 

256  drams  =  1  pound 

The  unit  of  measure  for  raw  silk  is  256,000  yards  per  pound.  Thus,  if 
1000  yards  —  one  skein  — of  raw  silk  weigh  one  dram,  or  if  256,000  yards 
weigh  one  pound,  it  is  known  as  1-dram  silk,  and  if  1000  yards  weigh 
two  drams,  the  yarn  is  called  2-dram  silk ;  hence  the  following  table  is 
made: 

1-dram  silk  =  1000  yards  per  dram,  or  256,000  yards  per  Ib. 
2-dram  silk  =  1000  yards  per  2  drams,  or  128,000  yards  per  Ib. 
4-dram  silk  =  1000  yards  per  4  drams,  or  64,000  yards  per  Ib. 


DRAMS  PER  1000  YARDS 

YARDS  PER  POUND 

YARDS  PER  OUNCE 

1 

256,000 

16,000 

1* 

204,800 

12,800 

1* 

p 

? 

If 

146,286 

9143 

2 

128,000 

8000 

2i 

113,777 

7111 

*i 

102,400 

6400 

2f 

93,091 

5818 

3 

? 

? 

8* 

78,769 

4923 

8* 

73,143 

4571 

Linen  Yarns.  —  The  sizes  of  linen  yarns  are  based  on  the  lea 
or  cuts  per  pound  and  the  pounds  per  spindle.  A  cut  is  300 
yards  and  a  spindle  14,000  yards.  A  continuous  thread  of 
several  cuts  is  a  hank,  as  a  10-cut  hank,  which  is  10  X  300  = 
3000  yards  per  hank.  The  number  of  cuts  per  pound,  or  the 
leas,  is  the  number  of  the  yarn,  as  30's,  indicating  30  x  300  = 
9000  yards  per  pound.  Eight-pound  yarn  means  that  a  spindle 
weighs  8  pounds  or  that  the  yarn  is  6-lea  (14,400  -5-  8)  -s-  300  =  6. 


CLOTHING  223 

Cotton  Yarns.  —  The  sizes  of  cotton  yarns  are  based  upon  the 
system  of  840  yards  to  1  hank.  That  is,  840  yards  of  cotton 
yarn  weighing  1  pound  is  called  No.  1  counts. 

Spun  Silk.  —  Spun  silk  yarns  are  graded  on  the  same  basis 
as  that  used  for  cotton  (840  yards  per  pound),  and  the  same 
rules  and  calculations  that  apply  to  cotton  apply  also  to  spun 
silk  yarns. 

Two  or  More  Ply  Yarns.  —  Yarns  are  frequently  produced  in 
two  or  more  ply ;  that  is,  two  or  more  individual  threads  are 
twisted  together,  making  a  double  twist  yarn.  In  this  case 
the  size  is  given  as  follows  : 

2/30's  means  2  threads  of  30's  counts  twisted  together,  and  3/30's 
would  mean  3  threads,  each  a  30's  counts,  twisted  together. 

(The  figure  before  the  line  denotes  the  number  of  threads  twisted  to- 
gether, and  the  figure  following  the  line  the  size  of  each  thread.) 

Thus  when  two  threads  are  twisted  together,  the  resultant 
yarn  is  heavier,  and  a  smaller  number  of  yards  are  required  to 
weigh  one  pound. 

For  example  :  30's 'worsted  yarn  equals  16,800  yd.  per  lb.,  but  a  two- 
ply  thread  of  30's,  expressed  2/30?s,  requires  only  8400  yards  to  the  pound, 
or  is  equal  to  a  15's ;  and  a  three-ply  thread  of  30's  would  be  equal  to  a 
10's. 

When  a  yarn  is  a  two-ply,  or  more  than  a  two-ply,  and  made 
up  of  several  threads  of  equal  counts,  divide  the  number  of  the 
single  yarn  in  the  required  counts  by  the  number  of  the  ply, 
and  the  result  will  be  the  equivalent  in  a  single  thread. 

To  Find  the  Weight  in  Grains  of  a  Given  Number  of  Yards 
of  Worsted  Yarn  of  a  Known  Count 

EXAMPLE.  —  Find  the  weight  in  grains  of  125  yards  of  20's 
worsted  yarns. 

No.  1's  worsted  yam    =  560  yards  to  a  lb. 
No.  20' s  worsted  yarn  =  11,200  yards  to  a  lb. 
1  lb.  worsted  yarn        =  7000  grains. 


224       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

If  11,200  yards  of  20's  worsted  yarn  weigh  7000  grains,  then  —  - 

1  1  j^UU 

of  7000  =  —  5—  x  7000  =  —  =  78.125  grains. 
11,200  8 

NOTE.  —  Another  method:    Multiply  the  given  number  of  yards  by 
7000,  and  divide  the  result  by  the  number  of  yards  per  pound  of  the 

given  count. 

125  x  7000  =  875,000. 
1  pound  20  's=  11,200. 
875,000  -T-  11,200  =  78.  125  grains.     Ans. 

To  Find  the  Weight  in  Grains  of  a  Given  Number  of  Yards 
of  Cotton  Yarn  of  a  Known  Count 

EXAMPLE.  —  Find  the  weight  in  grains  of  80  yards  of  20's 

cotton  yarn. 

No.  1's  cotton  =  840  yards  to  a  Ib. 
No.  20's  cotton  =  16,800  yards  to  a  Ib. 
1  Ib.  =  7000  grains. 

lyd.  20's  cotton  =J          grains. 


80  yd.  20's  cotton  =  x  80  =  —  =  33.33  grains.     Ans. 

16,800  21 

It  is  customary  to  solve  examples  that  occur  in  daily  practice 

by  rule. 

The  rule  for  the  preceding  example  is  as  follows  : 
Multiply  the  given  number  of  yards  by  7000  and  divide  the 

result  by  the  number  of  yards  per  pound  of  the  given  count. 

80  x  7000  =  560,000. 
560,000  -*-  (20  x  840)  =  33.33  grains.     Ans. 

NOTE.  —  7000  is  always  a  multiplier  and  840  a  divisor. 

To  find  the  weight  in  ounces  of  a  given  number  of  yards  of 
cotton  yarn  of  a  known  count,  multiply  the  given  number  of 
yards  by  16,  and  divide  the  result  by  the  yards  per  pound  of 
the  known  count. 

To  find  the  weight  in  pounds  of  a  given  number  of  yards 
of  cotton  yarn  of  a  known  count,  divide  the  given  number  of 
yards  by  the  yards  per  pound  of  the  known  count. 


CLOTHING  225 

To  find  the  weight  in  ounces  of  a  given  number  of  yards  of 
woolen  yarn  (run  system),  divide  the  given  number  of  yards 
by  the  number  of  runs,  and  multiply  the  quotient  by  100. 

NOTE.  —  Calculations  on  the  run  basis  are  much  simplified,  owing  to 
the  fact  that  the  standard  number  (1600)  is  exactly  100  times  the  number 
of  ounces  contained  in  1  pound. 

EXAMPLE.  —  Find  the  weight  in  ounces  of  6400  yards  of 
5-run  woolen  yarn. 

6400-  (5  x  100)=  12.8  oz.     Ans. 

To  find  the  weight  in  pounds  of  a  given  number  of  yards  of 
woolen  yarn  (run  system)  the  above  calculation  may  be  used, 
and  the  result  divided  by  16  will  give  the  weight  in  pounds. 

To  find  the  weight  in  grains  of  a  given  number  of  yards  of 
woolen  yarn  (run  system),  multiply  the  given  number  of  yards 
by  7000  (the  number  of  grains  in  a  pound)  and  divide  the 
result  by  the  number  of  yards  per  pound  in  the  given  run, 
and  the  quotient  will  be  the  weight  in  grains. 

EXAMPLES 

1.  How  many  ounces  are  there  (a)  in  6324  grains  ?     (6)  in 
341  pounds  ? 

2.  How  many  pounds  are  there  in  9332  grains  ? 

3.  How  many  grains  are  there  (a)  in  168J  pounds  ?     (6)  in 
2112  ounces  ? 

4.  Give   the   lengths  per  pound   of  the  following  worsted 
yarns  :  (a)  41's  ;  (6)  55's ;  (c)  105's ;  (d)  115's  ;  (e)  93's. 

5.  Give   the   lengths   per  pound   of   the  following   woolen 
yarns    (run  system):     (a)  9J's ;    (6)  6's ;    (c)  19's ;    (d)    17's ; 
(e)  li's. 

6.  Give  the  lengths  per  pound  of   the  following  raw  silk 
yarns  :  (a)  li's  ;  (6)  3's  ;  (c)  3J's  ;  (d)  20's  ;  (e)  28's. 

7.  Give  the  lengths   per  ounce    of   the  following   raw  silk 
yarns  :  (a)  4J's  ;  (b)  6|'s  ;  (c)  8's  ;  (d)  9's  ;  (e)  14's. 


226       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

8.  What  are  the  lengths  of  linen  yarns  per  pound :  (a)  8's  ; 
(b)  25's  ;  (c)  32's  ;  (cf)  28's  ;  (e)  45's  ? 

9.  What  are  the  lengths  per  pound  of  the  following  cotton 
yarns :  (a)  10's  ;  (b)  32's  ;  (c)  54's;  (d)  80's;  (e)  160;s? 

10.  What  are  the  lengths  per  pound  of  the  following  spun 
silk  yarns  :  (a)  30's  ;  (b)  45's  ;  (c)  38's  ;  (d)  29's  ;  (e)  42's  ? 

11.  Make  a  table  of  lengths  per  ounce  of  spun  silk  yarns 
from  1's  to  20's. 

12.  Find  the  weight  in  grains  of  144  inches  of  2/20's  worsted 
yarn. 

13.  Find  the  weight  in  grains  of  25  yards  of  3/30's  worsted 
yarn. 

14.  Find  the  weight  in  ounces  of  24,000   yards  of  2/40's 
cotton  yarn. 

15.  Find  the  weight  in  pounds  of  2,840,000  yards  of  2/60's 
cotton  yarn. 

16.  Find  the  weight  in  ounces  of  650  yards  of  li-run  woolen 
yarn. 

17.  Find  the  weight  in  grains  of  80  yards  of  ^-run  woolen 
yarn. 

18.  Find  the  weight  in  pounds  of   64,000   yards  of  5-run 
woolen  yarn. 

Solve  the  following  examples,  first  by  analysis  and  then  by 
rule : 

19.  Find  the  weight  in  grains  of  165  yards  of  35's  worsted. 

20.  Find  the  weight  in  grains  of  212  yards  of  40's  worsted. 

21.  Find  the  weight  in  grains  of  118  yards  of  25's  cotton. 

22.  Find  the  weight  in  grains  of  920  yards  of  18's  cotton. 

23.  Find  the  weight  in  pounds  of  616  yards  of  16^'s  woolen. 

24.  Find  the  weight  in  grains  of  318  yards  of  184's  cotton. 

25.  Find  the  weight  in  grains  of  25  yards  of  30's  linen. 


CLOTHING  227 

26.  Find  the  weight  in  pounds  of  601  yards  of  60's  spun 
silk. 

27.  Find  the  weight  in  grains  of  119  yards  of  118's  cotton. 

28.  Find  the  weight  in  grains  of  38  yards  of  64's  cotton. 

29.  Find  the  weight  in  grains  of  69  yards  of  39's  worsted. 

30.  Find  the  weight  in  grains  of  74  yards  of  40's  worsted. 

31.  Find  the  weight  in  grains  of  113  yards  of  1^'s  woolen. 

32.  Find  the  weight  in  grains  of  147  yards  of  l|^s  woolen. 

33.  Find  the  weight  in  grains  of  293  yards  of  8's  woolen. 

34.  Find  the  weight  in  grains  of  184  yards  of  16^  's  worsted. 

35.  Find  the  weight  in  grains  of  91  yards  of  44's  worsted. 

36.  Find  the  weight  in  grains  of  194  yards  of  68's  cotton. 

37.  Find  the  weight  in  pounds  of  394  yards  of  180's  cotton. 

38.  Find  the  weight  in  pounds  of  612  yards  of  60's  cotton. 

39.  Find  the  weight  in  grains  of  118  yards  of  44's  linen. 

40.  Find  the  weight  in  pounds  of  315  yards  of  32's  linen. 

41.  Find  the  weight  in  grains  of  84  yards  of  25's  worsted. 

42.  Find  the  weight  in  grains  of  112  yards  of  20's  woolen. 

43.  Find  the  weight  in  grains  of  197  yards  of  16's  woolen. 

44.  Find  the  weight  in  grains  of  183  yards  of  18's  cotton. 

45.  Find  the  weight  in  grains  of  134  yards  of  28's  worsted. 

46.  Find  the  weight  in  grains  of  225  yards  of  34's  linen. 

47.  Find  the  weight  in  pounds  of  369  yards  of  16's  spun  silk. 

48.  Find  the  weight  in  pounds  of  484  yards  of  18's  spun  silk 

To  Find  the  Size  or  the  Counts  of  Cotton   Yam  of  Known 
Weight  and  Length 

EXAMPLE.  —  Find  the  size  or  counts  of  84  yards  of  cotton 
yarn  weighing  40  grains. 


228       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

Since  the  counts  are  the  number  of  hanks  to  the  pound, 

™0°.  x  84  =  14,700  yd.  in  1  Ib. 
40 

14,700  -4-  840  =  17.5  counts.     Ans. 

RULE.  —  Divide  840  by  the  given  number  of  yards ;  divide 
7000  by  the  quotient  obtained  ;  then  divide  this  result  by  the 
weight  in  grains  of  the  given  number  of  yards,  and  the 
quotient  will  be  the  counts. 

840  -=-  84  =  10. 
7000  -f-  10  =  700. 
700  -f-  40  =  17.5  counts.     Ans. 

To  Find  the  Run  of  a  Woolen  Thread  of  Known  Length 
and  Weight 

EXAMPLE.  —  If  50  yards  of  woolen  yarn  weigh  77.77  grains, 
what  is  the  run  ? 

1600  +  50  =  32. 
7000-32  =  218.75. 
218.75  -f-  77.77  =  2.812-run  yarn.     Ans. 

RULE.  —  Divide  1600  (the  number  of  yards  per  pound  of  1- 
run  woolen  yarn)  by  the  given  number  of  yards  ;  then  divide 
7000  (the  grains  per  pound)  by  the  quotient ;  divide  this 
quotient  by  the  given  weight  in  grains  and  the  result  will  be 
the  run. 

To  Find  the  Weight  in  Ounces  for  a  Given  Number  of  Yards  of 
Worsted  Yarn  of  a  Known  Count 

EXAMPLE.  —  What  is  the  weight  in  ounces  of  12,650  yards  of 
30's  worsted  yarn  ? 

12,650  x  16  =  202,400. 
202,400  -  16,800  =  12.047  oz.     Ans. 

RULE.  —  Multiply  the  given  number  of  yards  by  16,  and 
divide  the  result  by  the  yards  per  pound  of  the  given  count, 
and  the  quotient  will  be  the  weight  in  ounces. 


CLOTHING  229 

To  Find  the  Weight  in  Pounds  for  a  Given  Number  of  Yards 
of  Worsted  Yarn  of  a  Known  Count 

EXAMPLE.  —  Find  the  weight  in  pounds  of  1,500,800  yards 
of  40's  worsted  yarn. 

1,500,800  -4-  22,400  =  67  Ib.     Am. 

RULE.  —  Divide  the  given  number  of  yards  by  the  number 
of  yards  per  pound  of  the  known  count,  and  the  quotient  will 
be  the  desired  weight. 

EXAMPLES 

1.  If  108  inches  of  cotton  yarn  weigh  1.5  grains,  find  the 
counts. 

2.  Find  the  size  of  a  woolen  thread  72  inches  long  which 
weighs  2.5  grains. 

3.  Find   the  weight   in  ounces  of   12,650   yards  of  2/30's 
worsted  yarn. 

4.  Find  the  weight  in  ounces  of  12,650  yards  of  40's  worsted 
yarn. 

5.  Find  the  weight  in  pounds  of   1,500,800    yards    of  40's 
worsted  yarn. 

6.  Find   the  weight  in  pounds  of  789,600  yards  of  2/30's 
worsted  yarn. 

7.  What  is  the  weight  in  pounds  of  851,200  yards  of  3/60's 
worsted  yarn  ? 

8.  If  33,600  yards  of  cotton  yarn  weigh  5  pounds,  find  the 
counts  of  cotton. 

Buying  Yarn,  Cotton,  Wool,  and  Rags 

Every  fabric  is  made  of  yarn  of  definite  quality  and  quan- 
tity. Therefore,  it  is  necessary  for  every  mill  man  to  buy 
yarn  or  fiber  of  different  kinds  and  grades.  Many  small  mills 
buy  cotton,  wool,  yarn,  and  rags  from  brokers  who  deal  in 
these  commodities.  The  prices  rise  and  fall  from  day  to  day 


230       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

according  to  the  law  of  demand  and  supply.  Price  lists 
giving  the  quotations  are  sent  out  weekly  and  sometimes 
daily  by  agents  as  the  prices  of  materials  rise  or  fall.  The 
following  are  quotations  of  different  grades  of  cotton,  wool, 
and  shoddy,  quoted  from  a  market  list : 

QUANTITY  PRICE  PER  LB. 

8103  lb.  white  yarn  shoddy  (best  all  wool) $0.485 

3164  Ib.  white  knit  stock  (best  all  wool) 365 

2896  Ib.  pure  indigo  blue 315 

1110  Ib.  fine  dark  merino  wool  shoddy 225 

410  Ib.  fine  light  merino  woolen  rags 115 

718  Ib.  cloakings  (cotton  warp) ,    .     .     .     .          .02 

872  Ib.  wool  bat  rags 035 

96  Ib.  2/20's  worsted  (Bradford)  yarn 725 

408  Ib.  2/40's  Australian  yam 1.35 

593  Ib.  1/50's  delaine  yarn 1.20 

987  Ib.  16-cut  merino  yarn  (50  %  wool  and  50  %  shoddy)      .     .          .285 
697  Ib.  carpet  yarn,  60  yd.  double  reel,  wool  filling 235 

Find  the  total  cost  of  the  above  quantities  and  grades  of 
textiles. 

EXAMPLES 

1.  The  weight  of  the  fleece  on  the  average  sheep  is  8  Ib. 
Wyoming  has  at  least  4,600,000  sheep ;  what  is  the  weight  of 
wool  raised  in  a  year  in  this  state  ? 

2.  A  colored  man  picks  155  Ib.  of  cotton  a  day ;  how  much 
cotton  will  he  pick  in  a  week  (6  days)  ? 

3.  The  average  yield  is  558  Ib.  per  acre ;  how  much  cotton 
will  be  raised  on  a  farm  of  165  acres  ? 

4.  The  standard  size  of  a  cotton  bale  in  the  United  States 
is  54  x  27  x  27  inches  ;  what  is  the  cubical  contents  of  a  bale  ? 

5.  In  purchasing  cotton  an  allowance  of  4  %  is  made  for 
tare.     How  much  cotton  would  be  paid  for  in  96  bales,  500  Ib. 
to  each  bale  ? 


CLOTHING  231 

6.  Broadcloth  was  first  woven  in  1641.     How  many  years 
has  it  been  in  use  ? 

7.  The   length   of    "Upland"    cotton   varies   from   three- 
fourths  to  one  and  one-sixteenth  inches.     What  is  the  differ- 
ence in  length  from  smallest  to  largest  ? 

8.  If  a  sample  of  110  Ib.  of  cotton  entered  a  mill  and  68  Ib. 
were  made  into  fine  yarn,  what  is  the  per  cent  of  waste  ? 

9.  If  a  yard  of  buckram  weighs  1.8  ounces,  how  many 
yards  to  the  pound  ? 

10.  If  a  calico  printing   machine   turns   out   95   fifty-yard 
pieces  a  day,  how  many  are  printed  per  hour  in  a  ten-hour  day  ? 

11.  If  a  sample   of   linen  weighing  one  pound  and  a  half 
absorbs  12  %  moisture,  what  is  the  weight  after  absorption  ? 

12.  A  piece  of  silk  weighing  3  Ib.  4  oz.  is  "  weighted  "  175%  ; 
what  is  the  total  weight  ? 

13.  If   the   textile    industry    in   a   certain    year   pays    out 
$  500,000,000  to  994,875  people,  what  is  the  wage  per  capita  ? 

14.  How  much  dyestuff,  etc.,  will  be  required  to  dye  5  Ib.  of 
cotton  by  the  following  receipt  ? 

6  °/o  brown  color,  afterwards  treated  with 

1.5  %  sulphate  of  copper, 
1.5  %  bichromate  of  potash, 
3  °/o  acetic  acid. 

15.  How  many  square  yards  of  cloth  weighing  8  oz.  per  sq. 
yd.  may  be  woven  from  1050  Ib.  of  yarn,  the  loss  in  waste  be- 
ing 5  per  cent  ? 

16.  A  piece  of  union  cloth  has  a  warp  of  12's  cotton  and  is 
wefted  with  30's  linen  yarn,  there  being  the  same  number  of 
threads  per  inch  in  both  warp  and  weft ;  what  percentage  of 
cotton  and  what  of  linen  is  there  in  the  cloth  ? 

17.  A   sample  of  calico  3  in.  by  4  in.  weighs  30  grains. 
What  is  the  weight  in  pounds  of  a  70-yard  piece,  36  in.  wide  ? 


232       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

18.  4  yd.  of  a  certain  cloth  contains  2  Ib.  of  worsted  at  67 
cents  a  pound  and  1£  Ib.  of  cotton  at  18  cents  a  pound.     Each 
is  what  per  cent  of  the  total  cost  of  material  ? 

19.  A  bale  of  worsted  weighing  75  Ib.  loses  8  oz.  in  reeling 
off ;  what  is  the  per  cent  of  loss  ? 

20.  If  Ex.  19  worsted  gains  0.45  Ib.  to  the  75  Ib.  bale  in  dye- 
ing, what  is  the  per  cent  of  gain  ? 

21.  This  75  Ib.  cost  $  50.25  and  it  lost  4  oz.  in  the  fulling 
mill,  what  was  the  value  of  the  part  lost  ? 

22.  The  total  loss  is  what  per  cent  of  the  original  weight  ? 
What  is  its  value  at  67  cents  a  pound  ? 


PART  IV  — THE  OFFICE  AND  THE   STORE 

CHAPTER   XI 
ARITHMETIC  FOR  OFFICE  ASSISTANTS 

EVERY  office  assistant  should  be  quick  at  figures  —  that 'is, 
should  be  able  to  add,  subtract,  multiply,  and  divide  accurately 
and  quickly.  In  order  to  do  this  one  should  practice  addition, 
subtraction,  multiplication,  and  division  until  all  combinations 
are  thoroughly  mastered. 

An  office  assistant  should  make  figures  neatly  so  that  there 
need  be  no  hesitation  or  uncertainty  in  reading  them. 

Rapid  Calculations 

Add  the  following  columns  and  check  the  results.  Compare 
the  time  required  for  the  different  examples. 

1.   27  2.    37  3.   471  4.    568  5.    1,039 

12  20  295  284  579 

8  11  194  187  381 

18  20  327  341  668 

12  16  287  272  559 

8  12  191  184  375 

8  16  237  193  430 

8,  9  194  156  350 

7  12  169  166  335 

11  15  247  232  479 

12  13  194  180  374 
2                        3                       27                      25  52 

12  17  253  240  493 

11  14  241  212  453 

12  20  355  367  722 
12  14  244  222  466 

8  11  93  79  172 
10  15  208  213  421 

233 


234       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


.  7 

7.  7 

8.  159 

9.  152 

10.  311 

2 

5 

60 

78 

138 

4 

7 

111 

88 

199 

6 

10 

173 

121 

294 

4 

6 

112 

84 

196 

4 

4 

88 

76 

164 

4 

5 

104 

83 

187 

4 

6 

96 

104 

200 

4 

7 

120 

97 

217 

8 

9 

144 

123 

267 

4 

5 

60 

101 

161 

4 

5 

73 

92 

165 

8 

10 

186 

176 

362 

4 

4 

64 

75 

139 

4 

6 

114 

113 

227 

4 

4 

89 

88 

177 

6 

7 

91 

80 

171 

8 

9 

204 

170 

374 

4 

13 

175 

166 

341 

4 

4 

73 

77 

150 

4 

7 

119 

127 

246 

4 

5 

84 

103 

187 

8 

11 

177 

165 

342 

6 

8 

156 

136 

292 

3 

4 

94 

61 

155 

12 

18 

310 

293 

603 

8 

12 

191 

189 

380 

8 

13 

268 

198 

466 

2 

2 

17 

17 

34 

4 

8 

122 

137 

259 

8 

0 

193 

185 

378 

1 

1 

4 

6 

10 

1 

1 

9 

15 

24 

1 

2 

16 

16 

32 

1 

1 

11 

15 

26 

1 

2 

34 

44 

78 

1 

2 

27 

34 

61 

1 

2 

26 

53 

79 

1 

2 

36 

41 

76 

1 

2 

17 

10 

27 

1 

2 

38 

22 

60 

ARITHMETIC   FOR   OFFICE   ASSISTANTS 


235 


11.  $162.24 

12.  $37,000.00 

13.  §31.25 

14.  $8,527.08 

15.  $630.33 

266.45 

300,000.00 

73.70 

2,907.31 

408.32 

277.56 

410,000.00 

2.00 

3,262.68 

399.99 

12,171.44 

82,000.00 

425 

8,096.90 

28.00 

17.72 

.89 

9,359.21 

644.15 

6.00 

51,000.00 

31.15 

2,177.30 

18,000.00 

33.15 

40,000.00 

3.20 

8,385.50 

32.85 

23.65 

16.75 

7,229.20 

154.65 

3.18 

34,500.00 

4.51 

8,452.38 

82.35 

3,066.34 

1,758.13 

517.50 

17,000.00 

2,665.76 

5,236.32 

25.00 

1128.13 

6,147.42 

639.24 

36.00 

15,500.00 

3.20 

4,443.88 

2.60 

30.00 

3,386.72 

79.90 

4.00 

5,500.00 

3,927.78 

1,143.00 

289.22 

1,000.00 

29.12 

4,797.46 

265.50 

2,612.00 

727.00 

17.82 

70,500.00 

1.00 

2,476.31 

141.33 

199.87 

33.27 

3,705.00 

2314.76 

10,000.00 

19.09 

6,417.42 

3,091.72 

2.40 

12,500.00 

720.00 

1,574.50 

1,049.95 

9.25 

1,500.00 

28.80 

3,121.97 

166.64 

55.80 

300.00 

96.00 

120.00 

494.03 

3.41 

26,146.93 

1,483.84 

18.00 

800.00 

5.00 

51.397.19 

657.62 

1.55 

50.00 

7.37 

99.55 

1,416.68 

3.15 

100.00 

3.60 

3,605.93 

135.50 

2.55 

200.00 

22,830.14 

208.33 

4,010.92 

250.00 

9.08 

85,706.13 

42.84 

126.45 

300.00 

36,361.19 

362.25 

2.25 

4.50 

39,056.23 

234.47 

152.70 

2,000.00 

30,000.00 

31.50 

10.25 

35.84 

179,346.77 

49.76 

3.62 

1,000.00 

3,375.31 

150.22 

4.00 

2.00 

12,638.85 

2.64 

111.10 

1,200.00 

3.50 

30,992.76 

2.40 

324.83 

11.06 

179,346.77 

22.50 

302.10 

114,350.00 

.74 

3,375.31 

8.92 

345.04 

40,000.00 

7.25 

12,638.85 

176.91 

301.10 

120,000.00 

6.00 

30,992.76 

11.30 

1.20 

9,476.00 

3.00 

16,503.48 

17.00 

236       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


16. 


$437.58 

2.75 

1.40 

70.06 

3.54 

396.89 

33.00 

18.24 

6.75 

68.70 

1.53 

9.20 

.90 

98.95 

117.13 

192.71 

58.43 

2.11 

2.92 

43.34 

5.80 

108.81 

1.75 

10.10 

3.25 

881.69 

82.80 

.75 

3.00 

26.50 

19.04 

2.24 

19.50 

2,676.35 

25.25 

.70 

36.53 

3.60 

3.00 

168.66 

67.60 


17. 


$81.33 

18.    $144.40 

19.   $61.45 

31.66 

15.00 

14.50 

9.91 

1,124.04 

1.80 

20.00 

110.59 

2.00 

23.25 

44.83 

24.17 

129.99 

318.40 

272.90 

9.01 

22.35 

5.13 

208.01 

757.00 

482.09 

150.98 

674.37 

.50 

14.50 

220.50 

10.60 

27.30 

36.60 

280.00 

6.50 

3.60 

83.78 

.32 

2.50 

36.90 

216.60 

31.00 

245.00 

40.00 

91.87 

481.30 

542.25 

18.97 

57.96 

25.49 

59.35 

53.07 

3.75 

2.54 

8.14 

1,863.74 

36.08 

155.70 

21.25 

22.38 

1,076.82 

6.47 

8,699.46 

449.85 

132.28 

4,437.97 

4.00 

391.00 

394.48 

3.00 

72.00 

24.00 

35.00 

85.12 

10.00 

310.49 

47.90 

10.40 

1,078.50 

31.68 

.85 

49.50 

37.70 

77.91 

39.76 

64.43 

17.21 

2.20 

158.26 

185.99 

1.50 

2.40 

6.00 

53.49 

8.62 

2.50 

7.50 

3.85 

1.70 

5.05 

23.65 

2.00 

7.60 

259.00 

.70 

2.00 

701.47 

92.00 

11,50 

3,148.00 

ARITHMETIC   FOR   OFFICE   ASSISTANTS         237 

Horizontal  Addition 

Reports,  invoices,  sales  sheets,  etc.,  are  often  written  in  such 
a  way  as  to  make  it  necessary  to  add  figures  horizontally.  In 
adding  figures  horizontally,  it  is  customary  to  add  from  left  to 
right  and  check  the  answer  by  adding  from  right  to  left. 

EXAMPLES 

Add  the  following  horizontally  : 

1.  38  +  76  +  49  = 

2.  11  +  43  +  29  =  - 

3.  27  +  57  +  15  = 

4.  34  +  16  +  23  = 

5.  47  +  89  +  37  = 

6.  53  +  74  +  42  = 

7.  94  +  17  +  67  = 

8.  79  +  37  +  69  = 

9.  83  +  49  +  74  = 

10.  19  -f  38  +  49  = 

Add  the  following  and  check  by  adding  the  horizontal  and 
vertical  totals  : 

11.  36  +  74  -|-  19  +  47  = 
29  +  63  -f  49  +  36  = 

+       +       4-       = 

12.  74  +  34  +  87  +  27  = 
37  +  19  +  73  +  34  = 

+      +      4-      = 

13.  178+    74  +  109+    83  = 

39  +  111  +  381  +  127  = 
+         +         +        = 

14.  217+589  +  784  = 
309  +  611  +  983  = 

+         +         = 


238       VOCATIONAL   MATHEMATICS   FOR   GIRLS 


15. 


1118  +  3719  +  8910  = 
3001  +  5316  +  6715  = 

+    +    = 


Add  the  following  and  check  by  adding  horizontal  and  verti- 
cal totals.    Compare  the  time  required  for  the  different  examples. 


16.  $702,000   $14,040  $370,000 

$6,475.00 

$1,072,000 

$20,515.00 

525,000 

10,500 

20,000 

350.00 

565,000 

11,300.00 

1,267,500 

25,350 

447,250 

7,826.88 

1,724,750 

33,401.88 

333,000 

6,660 

340,000 

5,950.00 

833,000 

16,022.50 

380,000 

7,600 

351,000 

6,142.50 

790,000 

15,070.00 

1,077,000 

21,540 

50,000 

875.00 

1,127,000 

22,415.00 

702,000 

14,040 

370,000 

6,475.00 

1,072,000 

20,515.00 

525,000 

10,500 

20,000 

350.00 

565,000 

11,300.00 

1,264,500 

25,290 

447,250 

7,826.87 

1,721,750 

33,341.87 

333,000 

6,660 

200,000 

3,500.00 

693,009 

13,572.50 

355,000 

7,100 

348,000 

6,090.00 

758,000 

14,427.50 

1,072,000 

21,440 

50,000 

875.00 

1,122,000 

22,315.00 

17.  318,143 

28,760 

9.04 

491.86 

189.54 

77,751,393 

295,187 

18,363 

6.22 

498.23 

188.74 

78,426,000 

300,789 

23,398 

7.95 

479.80 

187.88 

75,180,746 

279,735 

22,290 

7.97 

511.43 

187.24 

79,864,039 

302,737 

28,699 

9.48 

523.55 

187.80 

82,001,180 

302,338 

22,149 

7.33 

578.00 

188.83 

91,025,879 

341,085 

27,765 

8.14 

554.30 

192.87 

89,161,101 

335,775 

24,080 

7.17 

534.23 

192.13 

85,603,137 

311,739 

20,356 

6.53 

521.79 

192.17 

83,627,195 

335,350 

21,299 

6.35 

524.17 

192.76 

84,266,576 

281,481 

18,032 

6.41 

500.09 

194.89 

81,283,747 

305,370 

20,865 

6.83 

496.12 

196.06 

81,122,570 

18.  380,782,151 

451,880 

,223  520 

,781,017  389,692,401  1 

,743,135,792 

452,491,808 

480,722 

,907  537 

,837,574  481 

,528,491  1 

,952,580,780 

71,709,667 

28,842,684   17 

,056,557   91 

,836,090 

209,444,988 

1,585 

600 

317 

1,907 

1,102 

283,448,988 

282,640,795  326 

,233,015  291 

,835,151  1 

,184,157,949 

.  6,264 

5 

,879 

6,066 

6,061 

6,068 

97,333,163 

169,239 

,428  194 

,548,002   97 

,857,250 

558,977,843 

ARITHMETIC   FOR   OFFICE   ASSISTANTS 


239 


19.       3,200,000 

17,000,000 

28,000,000 

7,000,000 

55,700,000 

27,200,000 

25,000,000 

31,400,000 

23,000,000 

106,600,000 

6,100,000 

6,100,000 

850,000 

65,100,000 

64,200,000 

12,300,000 

142,450,000 

3,500,000 

12,000,000 

15,500,000 

625,000 

5,200,000 

2,900,000 

8,725,000 

1,416,353 

7,263,712 

2,000,000 

11,866,463 

22,546,528 

665,907 

542,539 

443,392 

415,531 

1,967,359 

3,500,000 

11,200,000 

13,200,000 

7,400,000 

35,300,000 

12,500,000 

2,500,000 

3,500,000 

2,600,000 

21,100,000 

20.     29,000,000 

22,500,000 

14,200,000 

16,600,000 

82,300,000 

13,500,000 

10,200,000 

9,600,000 

8,600,000 

41,900,000 

327,998 

330,915 

508,266 

358,262 

1,525,441 

1,122,905 

1,222,262 

1,296,344 

1,317,004 

4,958,515 

2,400,000 

1,100,000 

1,650,000 

1,800,000 

6,950,000 

1,500,000 

850,000 

900,000 

900,000 

4,150,000 

250,000 

305,000 

350,000 

300,000 

1,205,000 

Add  the  following  decimals  and  check 

the  answer 

: 

21.    21.51 

35.21 

36.17 

20.32 

28.30 

18.91 

12.42 

5.95 

20.95 

14.56 

15.85 

6.00 

3.17 

19.07 

11.02 

22.     44.33 

73.15 

71.59 

14.36 

8.15 

43.20 

47.14 

126.04 

85.05 

70.42 

93.35 

80.13 

31.15 

62.51 

49.17 

49.17 

-     29.37 

47.25 

31.10 

206.38 

37.59 

47.25 

35.59 

50.47 

73.26 

23.   On  the  following  page  is  an  itemized  list  of   invest- 
ments. 

What  is  the  total  amount  of  investments  ? 
What  is  the  average  rate  of  interest  ? 

Review  Interest,  page  50. 


240       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


List  of  Investments  Held  by  the  Sinking  Funds  of  Fall  Ewer,  Mass. 
January  1,  1913 


NAME 

KATE 

MATURITY 

AMOUNT 

City  of  Boston  Bonds 

34 

July  1,      1939 

$15,000 

City  of  Cambridge  Bonds 

»i 

Nov.  1,     1941 

25,000 

City  of  Chicago  Bonds 

4 

Jan.  1,      1921 

27,500 

City  of  Chicago  Bonds 

4 

Jan.  1,      1922 

100,000 

City  of  Los  Angeles  Bonds 

4* 

June  1,     1930 

50,000 

City  of  So.  Norwalk  Bonds 

4 

July  1,      1930 

23,000 

City  of  So.  Norwalk  Bonds 

4 

Sept.  1,     1930 

22,000 

City  of  Taunton  Bonds 

4 

June  1,     1919 

39,000 

Town  of  Revere  Note 

4.35  disc. 

Aug.  13,  1913 

10,000 

Boston  &  Albany  R.  R.  Bonds 

4 

May  1,      1933 

57,000 

Boston  &  Albany  R.  R.  Bonds 

4 

May  1,      1934 

57,000 

Boston  Elevated  R.  R.  Bonds 

4 

May  1,      1935 

50,000 

Boston  Elevated  R.  R.  Bonds 

44 

Oct.  1,      1937 

68,000 

Boston  Elevated  R.  R.  Bonds 

44 

Nov.  1,     1941 

50,000 

Boston  &  Lowell  R.  R.  Bonds 

4 

April  1,    1932 

16,000 

Boston  &  Maine  R.  R.  Bonds 

*4 

Jan.  1,      1944 

150,000 

Boston  &  Maine  R.  R.  Bonds 

4 

June  10,    1913 

20,000 

C.  B.  &  Q.  R.  R.  Bonds  (111.  Div.) 

4 

July  1,      1949 

50,000 

C.  B.  &  Q.  R.  R.  Bonds  (111.  Div.) 

3| 

July  1,      1949 

55,000 

Chi.  &  N.  W.  R.  R.   Bonds 

7 

Feb.  1,      1915 

92,000 

Chi.  &  St.  P.,  M.  &  O..  R.  R.  Bonds 

6 

June  1,     1930 

20,000 

Cleveland  &  Pittsburg  R.  R.  Bonds 

44 

Jan.  1,      1942 

35,000 

Cleveland  &  Pittsburg  R.  R.  Bonds 

4£ 

Oct.  1,      1942 

10,000 

Fitchburg  R.  R.  Bonds 

34 

Oct.  1,      1920 

50,000 

Fitchburg  R.  R.  Bonds 

34 

Oct.  1,      1921 

20,000 

Fitchburg  R.  R.  Bonds 

44 

May  1,      1928 

50,000 

Fre.  Elk.  &  Mo.  Val.  R.  R.  Bonds 

6 

Oct.  1,      1933 

85,000 

Great  Northern  R.  R.  Bonds 

4J 

July  1,      1961 

25,000 

Housatonic  R.  R.  Bonds 

5 

Nov.  1,     1937 

46,000 

Louis.     &     Nash.     R.  R.     Bonds 

(N.  O.  &  M.) 

6 

Jan.  1,      1930 

20,000 

Louis.     &     Nash.      R.  R.     Bonds 

(St.  L.  Div.) 

6 

March  1,  1921 

5,000 

Louis.     &     Nash.     R.  R.     Bonds 

(N.  &  M.) 

44 

Sept.  1,     1945 

10,000 

Louis.  &  Nash.  R.  R.  Bonds 

5 

Nov.  1,      1931 

35,000 

Mich.  Cent.  R.  R.  Bonds 

5 

March  1,  1931 

37,000 

Mich.  Cent.  R.  R.  Bonds 

(Kal.  &  S.  H.) 

2 

Nov.  1,     1939 

50,000 

ARITHMETIC   FOR   OFFICE   ASSISTANTS 


241 


24.    What  is  total  amount  of  the  following  water  bonds? 
What  is  the  average  rate  of  interest  ? 

Water  Bonds  of  Fall  River,  Mass. 


DATE  OF  ISSUE 

KATE 

TERM 

MATURITY 

AMOUNT 

June  1,  1893 

4 

30  years 

June  1,  1923 

$  75,000 

May    1,  1894 

4 

30  years 

May   1,  1924 

25,000 

Nov.   1,  1894 

4 

29  years 

Nov.   1,  1923 

25,000 

Nov.   1,  1894 

4 

30  years 

Nov.   1,  1924 

25,000 

May   1,  1895 

4 

30  years 

May   1,  1925 

25,000 

June  1,  1895 

4 

30  years 

June  1,  1925 

50,000 

Nov.    1,  1895 

4 

30  years 

Nov.  1,  1925 

25,000 

May    1,  1896 

4 

30  years 

May   1,  1926 

25,000 

Nov.   1,  1896 

4 

30  years 

Nov.  1,  1926 

25,000 

April  1,  1897 

4 

30  years 

April  1,  1927 

25,000 

Nov.    1,  1897 

4 

30  years 

Nov.  1,  1927 

25,000 

April  1,  1898 

4 

30  years 

April    ,  1928 

25,000 

Nov.    1,  1898 

4 

30  years 

Nov.     ,  1828 

25,000 

May    1,  1899 

4 

30  years 

May     ,  1929 

50,000 

Aug.  1,  1899 

4 

30  years 

Aug.     ,  1929 

150,000 

Nov.   1,  1899 

3* 

30  years 

Nov.     ,  1929 

175,000 

Feb.    1,  1900 

3* 

30  years 

Feb.     ,  1930 

100,000 

May   1,  1900 

3* 

30  years 

May     ,  1930 

20,000 

April  1,  1901 

3| 

30  years 

April    ,1931 

20,000 

April  1,  1902 

3* 

30  years 

April    ,  1932 

20,000 

April  1,  1902 

3* 

30  years 

April    ,  1932 

50,000 

Dec.    1,  1902 

3| 

30  years 

Dec.    1,  1932 

50,000 

April  1,  1903 

3* 

30  years 

April  1,  1933 

20,000 

Feb.    1,  1904 

3£ 

30  years 

Feb.    1,  1934 

175,000 

May    2,  1904 

4 

30  years 

May  2,  1934 

20,000 

1.   33        2.   35 

3.   37        4.   3f 

7               9 

8               1 

8.   42 

9.   49         10.   46 

17 

18                19 

SUBTRACTION 

DRILL  EXERCISE 

5.    36 

9  7 


6.   32 

4 


7.   26 

9 


11.   43  12.   41 

16  15 


242       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


13.  45    14.  44    15. 

17       17 

364    16.  468 
126       329 

17.  566 

328 

18.  661      19.  363 
324         127 

20.  465 

228 

24.  200,000 
121,314 

21.  362 
129 

22.  865,900   23.  891,000 
697,148      597,119 

25.  30,071 

28,002 

26.  581,300   27.  481,111 
391,111      310,010 

28.  681,900 
537,349 

29.  868,434 
399,638 

30.  753,829   31.  394,287 
537,297      277,469 

32.  567,397 
297,719 

33.  487,196 
311,076 

34. 
38. 

291,903    35. 
187,147 

$  835.00 
119.00 

36.  $1100.44 
835.11 

37.  $2881.44 
1901.33 

$  3884.59  39. 
1500.45 

$  4110.59 
1744.43 

40.  $2883.40 
1918.17 

41.  $3717.17 
1999.18 

42.  $1911.84 
1294.95 

43.  $ 

2837.73     44. 
1949.94 

$  5887.93 
4999.99 

MULTIPLICATION 

DRILL  EXERCISE 
By  inspection,  multiply  the  following  numbers : 


1.  1600x900. 

2.  800  x  740. 

3.  360  x  400. 

4.  590  x  800. 

5.  1700  x  1100. 

6.  1900x700. 

7.  788,000  x  600. 

8.  49,009x400. 

9.  318,000x4000. 
10.  988,000  x  50,000. 


11.  80  x  11. 

12.  79  x  11. 

13.  187  x  11. 

14.  2100  x  11. 

15.  2855  x  11. 

16.  84x25. 

17.  116  x  50. 

18.  288  x  25, 

19.  198x25. 

20.  3884  x  25. 


"Review  rules  on  multiplication,  pages  8-9. 


ARITHMETIC   FOR   OFFICE   ASSISTANTS          243 

BILLS    (Invoices) 

When  a  merchant  sells  goods  (called  merchandise),  he  sends 
a  bill  (called  an  invoice)  to  the  customer  unless  payment  is 
made  at  the  time  of  the  sale.  This  invoice  contains  an  itemized 
list  of  the  merchandise  sold  and  also  the  following : 

The  place  and  date  of  the  sale. 

The  terms  of  the  sale  (usually  in  small  type)  —  cash  or  a 
number  of  days'  credit.  Sometimes  a  small  discount  is  given 
if  the  bill  is  paid  within  a  definite  period. 

The  quantity,  name,  and  price  of  each  item  is  placed  on  the 
same  line.  The  entire  amount  of  each  item,  called  the  exten- 
sion, is  placed  in  a  column  at  the  right  of  the  item. 

Discounts  are  deducted  from  the  bill,  if  promised. 

Extra  charges,  such  as  cartage  or  freight,  are  added  after 
taking  off  the  discount. 

Make  all  Checks  payable  to  We  handle  only  highest  grades 

Union  Coal  Company  of  Anthracite  and  Bitu- 

of  Boston  minous  Coals 

UNION   COAL  COMPANY 

40  CENTER  STREET 

BRANCH   EXCHANGE  TELEPHONE 
CONNECTING   ALL   WHARVES   AND   OFFICES 

SOLD  TO    L.  T.  Jones, 

5  Whitney  St. , 

Mattapan,  Mass. 

BOSTON,    Sept.  3,  1914. 

6000  Ib.  Stove  Coal          7.00     $21.00 
4000  "   Nut  7.25      14.50 

35.50 

REC'D  PAYMENT 

SEPT.  28,   1914 
UNION   COAL  CO. 


244       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

When  the  amount  of  the  bill  or  invoice  is  paid,  the  invoice 
is  marked. 

Received  payment, 
Name  of  firm. 

Per  name  of  authorized  person. 

This  is  called  receipting  a  bill. 

Ledger 

Whenever  an  invoice  is  sent  to  a  customer,  a  record  of  the 
transaction  is  made  in  a  book  called  a  ledger.  The  pages  of 
this  book  are  divided  into  two  parts  by  means  of  red  or  double 
lines.  The  left  side  is  called  the  debit  and  the  right  side  the 
credit  side.  At  the  top  of  each  ledger  page  the  name  of  a 
person  or  firm  that  purchases  merchandise  is  recorded.  The 
record  on  this  page  is  called  the  account  of  the  person  or  firm. 
When  the  person  or  firm  purchases  merchandise,  it  is  recorded 
on  the  debit  side.  When  merchandise  or  cash  is  received,  it  is 
recorded  on  the  credit  side.  The  date,  the  amount,  and  the 
word  Mdse.  or  cash  is  usually  written. 

We  debit  an  account  when  it  receives  value,  and  credit  an 
account  when  it  delivers  value. 

E.    D.    REDINGTON 


1917 

1917 

Jan.   2 

Cash 

109 

1000 

Jan.  1 

Acc't  to  Perkins 

114 

810 

Note,  60  ds. 

114 

1500 

2 

Mdse. 

100 

3057 

9 

Page's  Order 

115 

575 

10 

" 

100 

575 

25 

Cash 

109 

500 

22 

Order  to  Jenness 

115 

375 

27 

Mdse. 

93 

157 

~>0 

688.05 

1+81S 

31 

Browne's  Ace. 

115 

397 

53 

1130 

OS 

SPECIMEN  LEDGER  PAGE 


ARITHMETIC   FOR   OFFICE   ASSISTANTS 


245 


A  summary  of  the  debits  and  credits  of  an  account  is  called 
a  statement.  The  difference  between  the  debits  and  credits 
represents  the  standing  of  the  account.  If  the  debits  are 
greater  than  the  credits,  the  customer  named  on  the  account 
owes  the  merchant.  If  the  credits  are  greater  than  the  debits, 
then  the  merchant  owes  the  customer. 

EXAMPLES 

Balance  the  following  accounts  : 

BLANEY,  BROWN  &  CO. 


1917 

1917 

Jan.  14 

Cons't  #7 

177 

669 

98 

Jan.   6 

Mdse. 

171 

1303 

"     Co.  #/ 

179 

386 

25 

30 

Dft.  favor  Button 

180 

900 

28 

"  #1  53.23 

179 

1200 

7,~> 

LUDWIG  &  LONG 


1917 

1917 

Jan.  6 

Cons'  t  #2 

177 

1939 

60 

Jan.  6 

Cash 

172 

1000 

20 

"   #2   327.50 

177 

1327 

50 

15 

" 

172 

939 

28 

« 

172 

1000 

CHARLES  N.  BUTTON 


1917 

1917 

Jan.    7 

Mdse. 

168 

651 

88 

Jan.    9 

Ship't  Co.  #2 

177 

856 

67 

12 

Cash 

173 

1000 

24 

Cons't  #2       208.51 

176 

4699 

0!t 

20 

" 

173 

2000 

29 

Ship't  Co.  #1 

179 

795 

37 

30 

Dft.  on  Blaney,  B. 

180 

900 

246       VOCATIONAL   MATHEMATICS   FOR   GIRLS 


D.    K.    REED   &   SON 


1917 

1917 

Jan.   8 

Cons  't  #1 

177 

525 

42 

Jan.  8 

Note  at  60  ds. 

180 

525 

17 

Mdse. 

170 

202 

50 

17 

Cash 

172 

202 

26 

Cons'  t  £1 

177 

243 

7~> 

"        CO.  #7 

179 

206 

PROFIT  AND  LOSS 

(Review  Percentage  on  pages  50-56) 

A  merchant  must  sell  merchandise  at  a  higher  price  than  he 
paid  for  it  in  order  to  have  sufficient  funds  at  the  end  of  the 
transaction  to  pay  for  clerk  hire,  rent,  etc.  Any  amount  above 
the  purchasing  price  and  its  attendant  expenses  is  called 
profit ;  any  amount  below  purchasing  price  is  called  loss. 

A  merchant  must  be  careful  in  figuring  his  profit.  He 
must  have  a  set  of  books  so  arranged  as  to  show  what  caused 
either  an  increase  or  reduction  in  the  profits. 

There  are  certain  special  terms  used  in  considering  profit 
and  loss.  The  first  cost  of  goods  is  called  the  net  or  prime 
cost.  After  the  goods  have  been  received  and  unpacked,  and 
the  freight,  cartage,  storage,  commission,  etc.  paid,  the  cost 
has  been  increased  to  what  is  called  gross  or  full  cost.  The 
total  amount  received  from  the  sale  of  goods  is  called  gross 
selling  price.  The  sum  of  expenses  connected  with  the  sale  of 
goods  subtracted  from  the  gross  selling  price  is  called  the  net 
selling  price.  A  merchant  gains  or  loses  according  as  the  net 
selling  price  is  above  or  below  the  gross  cost. 

There  are  two  methods  of  computing  gain  or  loss,  each 
based  on  the  rules  of  percentage.  In  the  first  method,  the 
gross  cost  is  the  base,  the  per  cent  of  gain  or  loss  the  rate,  the 
gain  or  loss  the  percentage.  The  second  method  considers 
the  selling  price  the  base  and  will  be  explained  in  detail  later. 


ARITHMETIC   FOR   OFFICE   ASSISTANTS 


247 


EXAMPLES 
1.   Make  extensions  after  deducting  discounts  and  give  total : 

Credit  not  allowed  on  goods  returned  without  our  permission 

PETTINGELL-ANDREWS  COMPANY 

ELECTRICAL  MERCHANDISE 

General  Offices  and  Warerooms 
156  to   16O  PEARL  STREET   and  491    to  511    ATLANTIC   AVENUE 

Terms  :  30  Days  Net 
NEW   YORK,     Nov   17   1911 

SOLD    TO     City  of  Lowell  School   Dept,   Lowell,  Mass. 
SHIPPED  TO      Same  Lowell    Industrial   School,   Lowell,   Mass. 

SHIPPED    BY        B    &.    L       11/14/11  OUR    REG.    NO.        3786 

ORDER    REC'D         1 1/13/1  I  REELS  COILS  BUNDLES  CASES  BBLS. 


tl 
H 

00 

^  "D 

o>$> 

ORDER   No.    78158               REG.   No.   52108 

PRICE 

1 

\ 

#4  Comealong#  11293                                        Ea 

4  00 

15% 

1 

\ 

#14492  16"  Extension  Bit                                  Ea 

2  00 

50% 

36 

36 

2  oz  cans  Nokorode  Soldering  Paste             Doz 

2  00 

50% 

15 

15 

#8020  Cutouts                                                   Ea 

36 

40% 

2 

2 

#322  H  &  H  Snap  Sws                                      Ea 

76 

30% 

125 

125 

#9395  Pore  Sockets                                           Ea 

30 

» 

45% 

125 

125 

#  1999  Fuseless  Rosettes                                   Ea 

08 

45% 

100 

100 

0  C  Ball  Adjusters  for  Lp  Cord                         M 

7  00 

50 

50 

I"  Skt  Bushings                                                   C 

50 

200 

200 

Pr  #43031  Std  #328  #1  Single  Wire  Cleats   M  Pr 

2668 

40  o£) 

200 

200 

Pr  #43033  Single  Wire  Cleats                      M  Pr 

i  U  /O 

40  00 

40% 

2 

2 

Lb  White  Exemplar  Tape                                Lb 

45 

248       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


2.   Make  extensions  on  the  following  items  and  give  total : 

Goods  are  Charged  for  the  Convenience  of  Customers  and  Accounts  are  Rendered  Monthly 

R  A.  McWniRR  Co. 

DEPARTMENT    STORE 
FALL    RIVER,    MASS. 

A.  A.  MILLS,  Pres't  &  Treas. 
J.  H.  MAHONEY,  Supt. 
R.  S.  THOMPSON,  Sec'y. 

Purchases  for  .  Fall   River  Technical   High  School 

September,   1913  City 

No.  Order  Number  719 


DATB 

ARTICLES 

AMOUNTS 

DAILY  TOTAL 

CREDITS 

Sept  4 

2   Doz  C  Hangers 
2     "     Skirt     " 

90 
45 

5 
6 

120  Long  Cloth 
34$  Cambric 
522  B  Cambric 

15 
18 

100  B  Nainsook 

16 

24  Doz  Kerr  L  Twist 

120 

8  Doz  Tape  Measures 
84  "     W  Thread 

25 
51 

9 

1    10/12   Doz  Tape 
1   Gro  Tambo  Cotton 

25 
520 

£  Doz  Bone  Stillettos 

46 

I     "     Steel 

46 

40  Paper  Needles 
20      " 

8 

2   Doz  M   Plyers 
2  Boxes  Edge  Wire 
12      "       Even  Tie  Wire 

600 
125 
180 

24     "       Brace 

225 

2       "       Lace 

160 

2  Pk  Ribbon 

125 

2  Rolls  Buckram 

90 

13 

48  Yd  Cape  Net 
100  Crinoline 

15 
5 

125 

5 

ARITHMETIC   FOR   OFFICE   ASSISTANTS         249 


3.    Make  extensions  on  the  following  items  and  give  total : 

Goods  are   Charged  for  the   Convenience  of  Customers  and  Accounts  are  Rendered  Monthly 

R  A.  McWniRR  Co. 

DEPARTMENT    STORE 
FALL    RIVER,    MASS. 

A.  A.  MILLS,  Pres't  &  Treas. 
J.  H.  MAHONEY,  Vice-Pres't. 
R.  S.  THOMPSON,  Sec'y. 

Purchases  for  Fall   River  Public  Buildings 

September,   1913  City 

No.  For  Technical   High  School 


DATE 

ARTICLES 

AMOUNTS 

DAILY  TOTAL 

CKEDITS 

Sept  4 

1    Dinner  Set 

1700 

100  Knives 

9 

100   Forks 

9 

100   D  Spoons 

10 

100  Tea  Spoons 

09 

1   Doz  Glasses 

90 

8J   Doz  Tumblers 

45 

8£     "      Bowls 

96 

54  Crash 

111 

50      " 

31 

^   Doz  Napkins 

270 

i      „ 

415 

2  Table  Cloths 

360 

12 

120  Crash 

"i 

15 

2  Stock  Pots 

325 

1    Lemon  Squeezer 

14 

1    Doz  Teaspoons 

500 

1   Butter  Spreader 

75 

£  Doz  Forks 

625 

250       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

EXAMPLE.  —  A  real  estate  dealer  buys  a  house  for  $  4990 
and  sells  it  to  gain  $  50.  What  is  the  per  cent  of  gain  over 
cost? 

SOLUTION. ^L  x  100  =  —  =  UiT  %.    Ana. 

4990  499 

DRILL  EXERCISE 
Find  per  cent  of  gain  or  loss : 


1. 

Cost 

$1660 

Gain 

$175 

6. 

Cost 

$6110 

Loss 

$112 

2. 

$1845 

$135 

7. 

$5880 

$   65 

3. 

$  1997. 

75 

$  412.50 

8. 

$  3181. 

10 

$108. 

75 

4. 

$  2222. 

50 

$  319.75 

9. 

$  7181. 

49 

$213. 

(>0 

5. 

$  3880. 

11 

$  610.03 

10. 

$  3333. 

19 

$   28. 

<)<) 

EXAMPLES 

1.  A  dealer  buys  wheat  at  91  cents  a  bushel  and  sells  to 
gain  26  cents.     What  is  the  per  cent  of  gain? 

2.  A  farmer  sold  a  bushel  of  potatoes  for  86  cents,  and  gained 
20  cents  over  the  cost.     What  was  the  per  cent  of  gain  ? 

3.  Real  estate  was  sold  for  $  19,880  at  a  profit  of  $  3650. 
What  was  the  per  cent  of  gain  ? 

4.  A  provision  dealer  buys  smoked  hams  at  19  cents  a  pound 
and  sells  them  at  31  cents  a  pound.     What  is  the  per  cent  of 
gain? 

5.  A  grocer  buys  eggs  at  28  cents  a  dozen  and  sells  them 
at  35  cents  a  dozen.     What  is  the  per  cent  gain  ? 

6.  A  dealer  buys  sewing  machines  at  $22  each  and  sells 
them  at  $  40.     What  is  the  per  cent  gain  ? 

7.  A  dealer  buys  an  automobile  for  $  972  and  sells  it  for 
$  1472  and  pays  $  73.50  freight.     What  is  the  per  cent  gain  ? 


ARITHMETIC   FOR   OFFICE   ASSISTANTS         251 

DRILL  EXERCISE 
Find  the  per  cent  gain  or  loss  on  both  cost  and  selling  price  : 


1. 

Cost 

$1200 

Selling  Price 

$1500 

6. 

Co»t 

$2475 

Selling  Price 

$2360 

2. 

$1670 

$1975 

7. 

$1650 

$1490 

3. 

$2325 

$2980 

8. 

$  4111.50 

$  2880.80 

4. 

$  4250.50 

$  5875.75 

9. 

$4335.50 

$4660.60 

5. 

$  3888.80 

$  4371.71 

10. 

$  2880.17 

$  2551.60 

REVIEW  EXAMPLES 

1.  A  dealer  buys  46  gross  of  spools  of.  cotton  at  $11.12. 
He  sells  them  at  5  cents  each.     What  is  his  profit  ?     What  is 
the  per  cent  of  gain  on  cost  ?  on  selling  price  ? 

2.  Hardware  supplies  were  bought  at  $  119.75  and  sold  for 
$  208.16.     What  is  the  per  cent  of  gain  on  cost  and  on  selling 
price  ? 

3.  A   grocer   pays   $  840   f.o.b.    Detroit  for  an   automobile 
truck.     The  freight  costs  him  $  61.75.     What  is  'the  total  cost 
of  automobile  truck  ?     What   per  cent  of   the  total    cost  is 
freight  ? 

4.  A  dry  goods  firm  buys  900  yards  of  calico  at  5  cents  a 
yard,  and  sells  it  at  9  cents.     What  is  the  profit  ?     What  per 
cent  of  cost  and  selling  price  ? 

5.  A  grocer  buys  a  can  (81  qt.)  of  milk  for  55  cents  and  sells 
it  for  9  cents  a  quart.     What  is  the  per  cent  of  gain  ? 

EXAMPLES 

1.    A  dealer  sold  a  piano  at  a  profit  of  $  115,  thereby  gaining 
18  %  on  cost.     What  was  the  selling  price  ? 

SOLUTION.  —  If  $  115  =  18  %  of  cost,  which  is  100  %, 

1  %  =  JjJff5_  =  6.3889 
100%  =$  638.  89  cost 
Adding  115.00  profit 

$  753.89  selling  price. 


252       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

2.  A  dealer  sold  furniture  at  a  profit  of  $  98.     What  was 
the  cost  of  the  furniture,  if  he  sold  to  gain  35  %  ? 

3.  A  coal  dealer  buys  coal  at  the  wharf  and  sells  it  to  gain  $  2 
per  ton.     What  is  the  cost  per  ton  if  he  gains  31  %  ? 

4.  A  shoe  jobber  buys  a  lot  of  shoes  for  $  1265  and  sells  to 
gain  26  % .     What  is  the  selling  price  ? 

5.  An  electrician  buys  a  motor  for  $  48  and  sells  it  to  gain 
18  %.     What  is  the  selling  price? 

6.  A  pair  of  shoes  was  sold  to  gain  26  %,  giving  the  shoe 
dealer  a  profit  of  97  cents.     What  was  the  cost  price  ?    What 
was  the  selling  price  ? 

FORMULAS 

Gain  or  loss  =  Cost  x  rate  of  gain  or  loss 
Gain  or  loss 


Cost  = 


Rate  of  gain  or  rate  of  loss 
Selling  Price  =  Cost  (100  %  +  rate  of  gain)  or  (100  %  —  rate  of  loss) 
Cost  =         Selling  Price  Selling  Price 

~  100  %  +  rate  of  gain    (  r   100  °/o  -  rate  of  loss 

DRILL  EXERCISE 
Find  the  selling  price  in  each  of  the  following  problems : 


Sold  to  Lose 

Coat 

Sold  to  Gain 

Cost 

1.   16|% 

$96 

6.   37% 

$250 

2.   20% 

$115 

7.   33%, 

$  644.50 

3.   30% 

$48 

8.   41% 

$  841.75 

4.   19% 

$  112.50 

9.   29% 

$  108.19 

5.   201% 

$  187.75 

10.   221% 

$237.75 

COMPUTING    PROFIT  AND   LOSS 

Second  MetTiod.  —  Many  merchants  find  that  it  is  better  busi- 
ness practice  to  figure  per  cost  profit  on  the  selling  price  rather 
than  on  the  cost  price.  Many  failures  in  business  can  be 


ARITHMETIC   FOR   OFFICE   ASSISTANTS         253 

traced  to  the  practice  of  basing  profits  on  cost.  We  must  bear 
in  mind  that  no  comparison  can  be  made  between  per  cents  of 
profit  or  cost  until  they  have  been  reduced  to  terms  of  the 
same  unit  value  or  to  per  cents  of  the  same  base. 

To  illustrate  :  It  costs  $  100  to  manufacture  a  certain  article.  The 
expenses  of  selling  are  22  %.  For  what  must  it  sell  to  make  a  net 
profit  of  10%?  Most  students  would  calculate  $132,  taking  the  first 
cost  as  the  basis  of  estimating  cost  of  sales  and  net  profit.  The  average 
business  man  would  say  that  the  expenses  of  selling  and  cost  should  be 
quoted  on  the  basis  of  the  selling  price. 

SOLUTION.  —  Expenses  of  selling  =  22  % 
Profit  =  10% 

32  %  on  selling  price. 
.  •.  Cost  on  $  100  =  68  %  selling  price. 
100  %  =  .$  147  selling  price. 

EXAMPLE  1.  —  An  article  costs  $  5  and  sells  for  $  6.  What 
is  the  percentage  of  profit?  Ans.  16|  %. 

Process. — Six  dollars  minus  $5  leaves  $1,  the  profit.  One  dollar 
divided  by  $6,  decimally,  gives  the  correct  answer,  16|%. 

EXAMPLE  2.  —  An  article  costs  $  3.75.  What  must  it  sell 
for  to  show  a  profit  of  25  %  ?  Ans.  $  5. 

Process. — Deduct  25  from  100.  This  will  give  you  a  remainder  of 
75,  the  percentage  of  the  cost.  If  $3.75  is  75%,  1%  would  be  $3.75 
divided  by  75  or  5  cents,  and  100%  would  be  $5.  Now,  if  you  marked 
your  goods,  as  too  many  do,  by  adding  25  %  to  the  cost,  you  would  ob- 
tain a  selling  price  of  about  $4.69,  or  31  cents  less  than  by  the  former 
method. 

EXAMPLES 

1.  What  is  the  percentage  of  profit,  if  an  article  costs  $  8.50 
and  sells  for  $  10  ? 

2.  What  is  the  percentage  of  profit  on  an  automobile  that 
cost  $  810  and  sold  for  $  1215  ? 

3.  An  article  costs  $  840.     What  must  I  sell  it  for  to  gain 
30  %  ? 


254       VOCATIONAL   MATHEMATICS   FOR   GIRLS 


4.    A  case  of  shoes  is  bought  for  $  30.     For  what  must  I  sell 
them  to  gain  25  %  ? 

TABLE  FOR  FINDING  THE  SELLING  PRICE  OF  ANY  ARTICLE 


COST 

TO  DO 

NET  PER  CENT  PROFIT  DESIRED 

BUSINESS 

1 

2 

8 

9 

10 

11 

12 

13 

14 

15 

20 

25 

30 

35 

40 

50 

15% 

84 

88 

82 

81 

80 

79 

78 

77 

76 

7.-) 

74 

78 

7-2 

71 

7o 

65 

60 

55 

50 

4;, 

35 

16% 

88 

82 

81 

so 

79 

7^ 

77 

76 

7r» 

74 

78 

72 

71 

7(i 

til) 

64 

59 

64 

49 

44 

84 

17  % 

82 

81 

80 

79 

7s: 

77 

76 

75 

74 

78 

7'2 

71 

70 

69 

(is 

68 

58 

58 

4s 

48 

88 

18% 

si 

SI) 

79 

7s 

77 

76 

7.') 

74 

78 

72 

71 

7o 

(','.» 

68 

(17 

62 

57 

52 

47 

42 

'52 

19% 

80 

79 

7s 

77 

76 

75 

74 

7:', 

72 

71 

7o 

69 

68 

67 

66 

61 

56 

51 

4f, 

41 

81 

20% 

79 

78 

77 

76 

75 

74 

7:i 

1-1 

71 

70 

69 

68 

67 

66 

65 

60 

55 

50 

4,r> 

40 

80 

21% 

78 

77 

76 

78 

74 

73 

72 

71 

70 

69 

68 

67 

66 

66 

64 

59 

54 

49 

44 

89 

•2!) 

22% 

77 

76 

7:> 

74 

78 

72 

71 

70 

69 

68 

67 

66 

65 

64 

68 

58 

58 

4s 

4:', 

88 

•2s 

23% 

76 

75 

74 

78 

7'2 

71 

7o 

69 

68 

67 

66 

65 

(14 

€3 

62 

57 

52 

47 

4-2 

87 

27 

24% 

75 

74 

7:', 

7'.' 

71 

7<i 

69 

68 

67 

66 

65 

64 

68 

62 

61 

56 

51 

46 

41 

86 

2t> 

25% 

74 

73 

72 

71 

7(i 

f-9 

68 

67 

66 

65 

64 

68 

62 

(11 

tin 

55 

50 

45 

40 

85 

25 

The  percentage  of  cost  of  doing  business  and  the  profit  are 
figured  on  the  selling  price. 

Rule 

Divide  the  cost  (invoice  price  with  freight  added)  by  the 
figure  in  the  column  of  "  net  rate  per  cent  profit  desired  "  on 
the  line  with  per  cent  it  cost  you  to  do  business. 


EXAMPLE.  —  If  a  wagon  cost 
Freight  .     .     . 


$60.00 

1.20 

$  61.20 

You  desire  to  make  a  net  profit  of 5  per  cent 

It  costs  you  to  do  business 19  per  cent 

Take  the  figure  in  column  5  on  line  19,  which  is  76. 

76  j  $6 1.2000  [  $80. 52,  the  selling  price. 
608 
400 
380 
200 
152 


ARITHMETIC   FOR   OFFICE   ASSISTANTS         255 

Solve  the  following  examples  by  table : 

1.  I  bought  a  wagon  for    $84.00   f.o.b.  New   York   City. 
Freight  cost  $  1.05.     I  desire  to  sell  to  gain  8  %.     If  the  cost 
to  do  business  is  18  %,  what  should  be  the  selling  price? 

2.  I  buy  goods  at  $  97  and  desire  a  net  profit  of  7  % .     It 
costs  16  %  to  do  business.     What  should  be  my  selling  price  ? 

3.  Hardware  supplies  are   purchased   for    $489.75.     If   it 
costs  23  %  to  do  the  business,  and  I  desire  to  make  a  net  profit 
of  11  %,  for  what  must  I  sell  the  goods? 

EXAMPLES 

1.  I  bought  15  cuts  of  cloth  containing  40^  yd.   each,  at 
7  cents  a  yd.,  and  sold  it  for  9  cents  a  yd.     What  was  the 
gain? 

2.  A  furniture  dealer  sold  a  table  for  $  14.50,  a  couch  for 
$  45.80,  a  desk  for  $  11.75,  and  some  chairs  for  $  27.30.     Find 
the  amount  of  his  sales. 

3.  Goods  were  sold  for  $367.75  at  a  loss  of  $125.     Find 
the  cost  of  the  goods. 

4.  Goods  costing  $  145.25  were  sold  at  a  profit  of  $  28.50. 
For  how  much  were  they  sold  ? 

5.  A  woman  bought  4±  yards  of  silk  at  $  1.80  per  yard,  and 
gave  in  payment  a  $  10  bill.     What  change  did  she  receive.? 

6.  I  bought  25  yards  of  carpet  at  $  2.75  per  yard,  and  6 
chairs   at    $  4.50   each,   and   gave   in   payment   a    $  100  bill. 
What  change  should  I  receive  ? 

TIME    SHEETS    AND    PAY   ROLLS 

Office  assistants  must  tabulate  the  time  of  the  different  em- 
ployees and  compute  the  individual  amount  due  each  week. 
In  addition,  they  must  know  the  number  of  coins  and  bills  of 
different  denominations  required  so  as  to  be  able  to  place  the 
exact  amount  in  each  envelope.  This  may  be  done  by  making 
out  the  following  pay  roll  form. 


256       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

FORM  USED  TO  DETERMINE  THE  NUMBER  OF  DIFFERENT  DENOMINATIONS 


No,  Persons 

Amt,  Rec'd 

$10 

$5 

$2 

$1 
g 

50? 

g 

25? 

10? 

5? 

1? 

2 

13.50 

g 

g 

3 

<?.8<5 

S 

6 

3 

3 

3 

9- 

r.y-s 

¥• 

V- 

¥• 

S 

/g 

2 

<?./8 

2 

V- 

2 

g 

6 

Total  Number  Coins 

2 

<? 

/6 

2 

5 

7 

/3 

2 

IS 

TIME  CARD 


Week  Ending- 
No. 
NAME 


.191 


1 

Mou 
Tue 
Wed 

MORNING 

AFTERNOON 

LOST  OR 
OVERTIME 

_i 
<t 

IN 

OUT 

IN 

OUT 

IN 

OUT 













Thu 
Fri 

Sat 













Sun 

Total  Time--         Mrs. 

Rate 

Total  Wages  for  Week  $ 


FORM  USED  TO  SEND  TO  THE  BANI 
FOR  THE  MONEY  FOR  PAY  ROLL 


MEMORANDUM    OF 

CASH     FOR    PAY    ROLL 

WANTED    BY 

-19- 


Twenties  .... 
Tens     
Fives    
Twos    
Ones     
Halves  
Quarters   .... 
Dimes  
Nickels      .... 
Pennies     .... 
Total 



ARITHMETIC   FOR   OFFICE   ASSISTANTS         257 


TABLE   OF  WAGES1 

To  find  the  amount  due  at  any  rate  from  30  cents  to.  55 
cents  per  hour,  look  at  the  column  containing  the  number  of 
hours  and  the  amount  will  be  shown.  Time  and  a  half  is 
counted  for  overtime  on  regular  working  days,  and  double 
time  for  Sundays  and  holidays. 


M 

M 

P9 

n 

H 

H 

w 

H 

K 

W 

H 

i 

s 

g 

H 

- 

I 

3 

H 

s 

fa 

X 

H 

p 

S 

S 

1 

1 

I 

g 

M 

M 

§ 

i 

S 

M 

i 

e 

« 
H 

a 

K 

M 

M 

0 

Q 

K 

6 

Q 

tt 

M 

0 

Q 

%... 

$0  30 

$0  15 

$0  22* 

$0  30 

$0  32* 

$0  16} 

$024| 

$0  32* 

$0  45 

$0  22* 

$0  33f 

$0  45 

1... 

30 

30 

45 

60 

32* 

32* 

48} 

65 

45 

45 

67* 

90 

2... 

30 

60 

90 

1  20 

32* 

65 

97* 

1  80 

45 

90 

1  35 

1  80 

8... 

30 

90 

1  35 

1  80 

32* 

97* 

1  46£ 

1  95 

45 

1  35 

2  02* 

2  70 

4... 

30 

1  20 

1  80 

2  40 

32* 

1  30 

1  95 

2  60 

45 

1  80 

2  70 

3  60 

5... 

30 

1  50 

2  25 

3  00 

32* 

1  62* 

2  43| 

3  25 

45 

2  25 

3  37* 

4  50 

6... 

30 

1  SO 

2  70 

8  60 

82* 

1  95 

2  92* 

3  90 

45 

2  70 

4  05 

5  40 

7... 

30 

2  10 

3  15 

4  20 

82* 

2  27* 

3  41J 

4  55 

45 

3  15 

4  72* 

6  80 

8... 

30 

2  40 

3  60 

4  80 

32* 

2  60 

3  90 

5  20 

45 

3  60 

5  40 

7  20 

9... 

30 

2  70 

4  05 

5  40 

32* 

2  92* 

4  38| 

5  85 

45 

4  05 

6  07* 

8  10 

10... 

30 

3  00 

4  50 

6  00 

32* 

3  25 

4  87*. 

6  50 

45 

4  50 

6  75 

9  00 

%... 

$047* 

$023f 

$0  35f 

$0  47* 

$0  50 

$0  25 

$0  37* 

$0  50 

$0  55 

$0  27* 

$0  41J 

$0  55 

1... 

47* 

47* 

71} 

95 

50 

50 

75 

1  00 

55 

55 

82* 

1  10 

2... 

47* 

95 

1  42* 

1  90 

50 

1  00 

1  50 

2  00 

55 

1  10 

1  65 

2  20 

8... 

47* 

1  42* 

2  13J 

2  85 

50 

1  50 

2  25 

3  00 

55 

1  65 

2  47* 

3  30 

4... 

47* 

1  90 

2  85 

3  80 

50 

2  00 

3  00 

4  00 

.  55 

2  20 

8  30 

4  40 

5... 

47* 

2  37* 

3  56J 

4  75 

50 

2  50 

3  75 

5  00 

55 

2  75 

4  12* 

550 

6... 

47* 

2  85 

4  27* 

5  70 

50 

3  00 

4  50 

6  00 

55 

3  30 

4  95 

6  60 

7... 

47* 

3  32* 

4  98} 

6  65 

50 

3  50 

5  25 

7  00 

55 

3  85 

5  77* 

7  70 

8... 

47* 

3  80 

5  70 

7  60 

50 

4  00 

6  00 

8  00 

55 

4  40 

6  60 

8  80 

9... 

47* 

4  27* 

6  41i 

8  55 

50 

4  50 

6  75 

9  00 

55 

4  96 

7  42* 

9  90 

10... 

47* 

4  75 

7  12* 

9  50 

50 

5  00 

7  50 

10  00 

55 

5  50 

8  25 

11  00 

EXAMPLES 

1.   Find   the   amount   due   a  carpenter  who  has  worked   8 
hours  regular  time  and  2  hours  overtime  at  55  cents  per  hour. 

1  Similar  tables  may  be  constructed  for  other  rates. 


258       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

2.  A  plasterer  worked  on  Sunday  from  8  to  11  o'clock.     If 
his  regular  wages  are  45  cents  per  hour,  how  much  will  he 
receive  ? 

3.  A  machinist's  regular  wage  is  55  cents  an  hour.     How 
much  money  is  due  him  for  working  July  4th  from  8-12  A.M. 
and  1^.30  P.M.  ? 

4.  A  plumber  works  six  days  in  the  week ;  every  morning 
from  7.30  to  12  M.  ;  three  afternoons  from  1  to  4.30  P.M.  ;  two 
afternoons  from  1  to  5.30 ;  and  one  from  1  until  6  P.M.     What 
will  he  receive  for  his  week's  wages  at  50  cents  per  hour  ? 

WAGES  OF  EMPLOYEES 

Superintendent $1,200.00  per  annum 

Matron 700.00  per  annum 

Nurses,  2  at 45.00  per  month 

Nurses,  1  at 40.00  per  month 

Nurses,  3  at 35.00  per  month 

Attendant 6.00  per  week 

Cook 12.00  per  week 

Assistant  cook 1.00  per  day 

Kitchen  maid 6.00  per  week 

Ward  maids,  4  at 6.00  per  week 

Waitresses,  2  at 6.00  per  week 

Laundress 8.00  per  week 

Washwomen,  2  at 6.00  per  week 

Janitors,  1  day  and  1  night 16.00  per  week 

Barber    .     . 6.00  per  week 

5.  Find  the  total  of  coins  and  bills  of  all  different  denomi- 
nations necessary  to  make  up  the  weekly  pay  roll  (52  weeks 
=  a  year)  of  the  above.     Assume  full  time  for  a  week.     Make 
out  the  currency  memorandum  for  bank. 

6.  Find  the  total  of  coins  and  bills  of  the  different  denomi- 
nations necessary  to  make  up  the  following  pay  roll : 

47£  hours,  at  30  cents. 
48  hours,  at  45  cents. 
48  hours,  at  47|  cents. 
46  hours,  at  32^  cents. 


ARITHMETIC   FOR   OFFICE   ASSISTANTS 


259 


7.  Make  a  pay  roll  memorandum  for  the  following  pay 
roll: 

48  at  42|,  39  at  45,  46|  at  48£. 

TEMPORARY  LOANS 

The  following  is  a  statement  of  the  temporary  loans  of  a 
New  England  city  negotiated  during  the  year,  —  amount,  time, 
rates. 


DATE 

AMOUNT  OF 
LOAN 

TIME 

RATE  OF 
INTEREST 

AMOUNT  OF 
INTEREST 

Months 

Ehys 

Feb.  28 

$50,000 

243 

2.76 

Feb.  28 

25,000 

243 

2.76 

Feb.  28 

25,000 

243 

2.76 

June    6 

100,000 

5 

3.25 

June  19 

25,000 

126 

3.52 

June  19 

25,000 

126 

3.52 

June  19 

25,000 

126 

3.52 

June  19 

25,000 

126 

3.52 

July     3 

25,000 

124 

3.55 

July     3 

25,000 

124 

3.55 

July     3 

25,000 

124 

3.55 

July     3 

25,000 

124 

3.55 

July     3 

25,000 

124 

3.55 

July     3 

25,000 

124 

3.55 

Aug.  14 

25,000 

2 

4. 

Aug.  20 

25,000 

80 

4.07 

Aug.  20 

25,000 

80 

4.07 

Aug.  20 

25,000 

80 

4.07 

Aug.  20 

25,000 

80 

4.07 

Sept.    4 

25,000 

40 

4. 

Sept.    4 

25,000 

40 

4. 

Sept.    4 

16,000 

40 

4. 

Write  in  a  column  after  each  loan,  as  suggested  above,  the 
amount  of  interest  on  each  loan  for  the  time  and  at  the  rate. 


CHAPTER   XII 
ARITHMETIC  FOR  SALESGIRLS   AND  CASHIERS 

THE  majority  of  employees  in  a  department  store  are  sales- 
girls. It  may  be  well  to  describe  briefly  the  method  of 
operation  of  such  a  store  and  to  indicate  what  part  a  salesgirl 
has  in  it. 

A  department  store  is  a  combination  of  a  number  of  distinct 
stores  or  departments  under  one  roof  and  general  manage- 
ment. It  is  organized  in  this  way  for  the  purpose  of  economy. 
Each  department  is  conducted  as  a  separate  store,  and  is 
in  charge  of  a  buyer,  who  both  buys  and  plans  the  sales 
for  his  department.  His  department  is  charged  for  rent, 
according  to  its  location,  and  must  also  pay  for  overhead 
charges. 

The  buyer  in  charge  of  each  department  has  under  him 
salesgirls  or  saleswomen,  who  sell  the  goods.  Each  salesgirl 
has  a  book  containing  sales  slips  in  duplicate  and  a  card  to 
show  the  amount  of  sales. 

The  sales  slip  shows  the  name  and  address  of  the  purchaser 
if  the  merchandise  is  to  be  sent  to  the  customer's  home.  In 
the  case  of  a  charge  account  a  special  form  of  sales  slip  is 
used.  The  name  and  quality  of  the  article  purchased  are 
written  in  large  space  and  the  amount  extended  to  the  right. 
The  amount  of  money  received  from  the  purchaser  is  placed 
at  the  top  of  the  sales  slip. 

A  carbon  copy  of  each  sales  slip  is  made.  The  carbon  copy 
is  given  to  the  customer  and  the  original  is  sent  with  the  money 
to  the  cashier.  It  is  then  used  to  tabulate  data  in  regard  to 
sales,  etc. 

260 


ARITHMETIC   FOR   SALESGIRLS  AND   CASHIERS       261 


J.  * 

860( 

Name 
Addrei 

sou 

BY 

[.  EMKRSON  CO. 

;       Dallas,  Tex.,       19  -- 

In  Case  of  Error  Please  Return  Goods  and  Bill 

J-    » 

8606 

Name 
Addre& 

SOLI 
BY 

[.    1C  MIC  It  SON    CO. 

Dallas,  Tex.,       19  -- 

S-                      - 

D 

E 
)                       P                 AM'T 
T                  REC'D 

s 

D 

E 
>                        P                 AM'T 
__T                  REC'D 

Pur.  by                   \ 

$1 

Pur.  by 

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.fl'O.O 

So32 

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oo"S 

3a8- 

^ 

C0?  fl 

SS1_ 

Is4*00 



ce£2 

Am't  Rec'd          Sold  by         Am't  of  Sale 

Customers  tcill  please  report  any  failure 
to  deliver  bill  with  goods 

8606            1 

This  Slip  must  go  in  Customer's  Parrel.  Violation 
of  this  Rale  is  cause  for  Instant  Dismissal 

1 

SAI^KSMATS'S    VOUCHER. 

DEPARTMENT 

SALESMAN DATE-- 


Cash  Sales 

Charge  Sales 

Cash  Sales 

Charge  Sales 

1 

Forward 

2 

10 

3 

11 

4 

12 

5 

13 

6 

14 

7 

15 

8 

16 

9 

17 

262       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

Salesgirls  should  be  able  to  do  a  great  many  calculations  at 
sight.     This  ability  comes  only  through  practice. 

EXAMPLES 
Find  the  amount  of  the  following : 

1.  10  yd.  percale  at  121  cents. 

2.  12  yd.  voile  at  16 1  cents. 

3.  27  yd.  silesia  at  331  cents. 

4.  50  yd.  serge  at  $  1.50. 

5.  28  yd.  mohair  at  $  1.25. 

6.  48  yd.  organdie  at  37^-  cents. 

7.  911  yd.  gingham  at  10  cents. 

8.  112  yd.  calico  at  41  cents. 

9.  36  yd.  galatea  at  15  cents. 

10.  11  yd.  lawn  at  19  cents. 

11.  64  yd.  dotted  muslin  at  621  cents. 

12.  24  yd.  gabardine  at  $1.75. 

13.  18  yd.  poplin  at  29  cents. 

14.  16  yd.  hamburg  at  15  cents. 

15.  12  yd.  lace  at  871  cents. 

16.  19  yd.  val  lace  at  9  cents. 

17.  26  yd.  braid  at  25  cents. 

18.  48  dz.  hooks  and  eyes  at  12  cents0 

19.  19  yd.  cambric  at  15  cents. 

20.  18  pc.  binding  at  16  cents. 

21.  6  yd.  canvas  at  24  cents. 

22.  56  yd.  linen  at  621  cents. 

23.  18  yd.  albatross  at  $  1.50. 

24.  22  yd.  silk  at  $  2.25. 


ARITHMETIC   FOR   SALESGIRLS   AND    CASHIERS       263 

PROBLEMS 

1.  I  bought  cotton  cloth  valued  at  $  6.25,  silk  at  $  13.75, 
handkerchiefs  for  $  2.50,  and  hose  for  $  2.75.     What  was  the 
whole  cost  ? 

2.  Ruth  saved  $  15.20  one  month,  $  20.75  a  second  month, 
and  the  third  month   $  4.05  more  than  the  first  and  second 
months    together.      How   much   did    she*   save   in   the   three 
months  ? 

3.  Goods  were  sold  for  $  367.75,  at  a  loss  of  $  125.     Find 
the  cost  of  the  stock. 

4.  Goods  costing  $  145.25  were  sold  at  a  profit  of  $  28.50. 
For  how  much  were  they  sold  ? 

5.  A  butcher  sold  8J  pounds  of  meat  to  one  customer, 
9J-  pounds  to  a  second,  to  the  third  as  much  as  the  first  plus 
1£  pounds,  to  a  fourth  as  much  as  to  the  second.     How  many 
pounds  did  he  sell  ? 

6.  Edith  paid  $42.75  for  a  dress,  one-half  as  much  for  a 
cloak,  and  $  7.25  for  a  hat.     How  much  did  she  pay  for  all  ? 

7.  A  merchant  sold  four  pieces  of  cloth ;  the  first  piece 
contained  24  yards,  the  second  32  yards,  the  third  16  yards, 
and  the  fourth  five-eighths  as  many  yards  as  the  sum  of  the 
other  three.     How  many  yards  were' sold? 

8.  From  a  piece  of  cloth  containing  65f  yards,  there  were 
sold  23J  yards.     How  many  yards  remained  ? 

9.  A  merchant  sold  goods  for  $  528.40  and  gained  $  29.50. 
Find  the  cost. 

10.  From  11  yards  of  cloth,  3|  were  cut  for  a  coat,  and 
6J  yards  for  a  suit.     How  many  yards  remained  ? 

11.  I  bought  15  cuts  of  cloth  containing  40^  yards  each  at 
7  cents  a  yard  and  sold  it  for  9  cents  a  yard.     What  was  the 
gain? 


264       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

12.  What  is  the  cost  of  13-J  yards  of  silk  at  $  3.75  per  yard  ? 

13.  What  is  the  cost  of  16^  yards  of  broadcloth  at  $  2.25 
per  yard  ? 

14.  What  is  the  cost  of  3  pieces  of  cloth  containing  12|, 
14^,  and  15^  yards  at  121  cents  per  yard  ? 

15.  What  will  5|  yards  of  velvet  cost  at  $  2.75  per  yard  ? 

16.  What  is  the  cost  of  three-fourths  of  a  yard  of  crgpe  de 
chine  at  $  1.75  per  yard  ? 

17.  A  saleslady  is  paid  $  1.00  per  day  for  services  and  a 
bonus  of  2  %  on  all  sales  over  $  50  per  week.     If  the  sales 
amount  to  $  175  per  week,  what  will  be  her  salary  ? 

18.  At  $  1.33^  a  yard,  how  much  will  15  yards  of  lace  cost  ? 

19.  At  $  1.16 J  a  yard,  how  much  will  9  yards  of  silk  cost  ? 

20.  At  $  1.12^  per  yard,  how  much  will  6  yards  of  velvet 
cost? 

21.  At  33^  cents  each,  find  the  cost  of  101  handkerchiefs. 

22.  A  salesgirl  sold  141  yards  of  gingham  at  25  cents,  9 
yards  of  cotton  at  V2I\  cents,  101  yards  of  Madras  at  35  cents. 
Amount  received,  $  10.     How  much  change  will  be  given  to  the 
customer  ? 

23.  Sold  6£  yards  of  cheviot  at  $  1.10,  5f  yards  of  silk  at 
$  1.25,  91  yards  of  velveteen  at  98  cents.     Amount  received, 
$  25.00.     How  much  change  will  be  given  to  the  customer  ? 

24.  Sold  111  yards  of  Persian  lawn  at  $  1.95,  6|  yards  of 
dimity  at  25  cents,  12J'  yards  of  linen  suiting  at  75  cents. 
Amount  received,  $  40.     How  much  change  will  be  given  to 
the  customer  ? 

25.  Sold  9|  yards  of  Persian  lawn  at  $  1.371,  5J-  yards  of 
cheviot  at  $  1.25,  15  yards  of  cotton  at  121  cents.     Amount 
received,  $  30.     How  much  change  will  be  given  to  the  cus- 
tomer ? 


ARITHMETIC   FOR   SALESGIRLS  AND    CASHIERS       265 

26.  Sold  7  yards  of  muslin  at  25  cents,  12^  yards  of  lining 
at  11  cents,  6|  yards  of  lawn  at  $  1.50,  7  yards  of  suiting  at 
75  cents.     Amount  received,  $  20.     How  much  change  will  be 
given  to  the  customer  ? 

27.  Sold  16  yards  of  velvet  at  $  2.25,  14J  yards  of  suiting 
at  48  cents,  23  yards  of  cotton  at  15  cents,  6|  yards  of  dimity 
at  24  cents,  7|  yards  of  ribbon  at  25  cents.     Amount  received, 
$  50.     How  much  change  will  be  given  to  the  customer  ? 

28.  At  121  cents  a  yard,  what  will  8J  yards  of  ribbon  cost  ? 

29.  At  $  2.50  a  yard,  what  will  2.8  yards  of  velvet  cost  ? 

30.  If  it  takes  5^  yards  of  cloth  for  a  coat,  3i  yards  for  a 
jacket,  and  1  a  yard  for  a  vest,  how  many  yards  will  it  take 
for  all  ? 

31.  I  gave  $  16.50  for  33  yards  of  cloth.     How  much  did 
one  yard  cost  ? 

32.  Mary  went  shopping.     She  had  a  $  20  bill.     She  bought 
a  dress  for  $  9.50,  a  pair  of  gloves  for  $  .75,  a  fan  for  $  .87, 
two  handkerchiefs  for  $  .37  each,  and  a  hat  for  $  4.50.     How 
much  money  had  she  left  ? 

33.  Emma's  dress  cost  $  11.25,  and  Mary's  cost  f  as  much. 
How  much  did  Mary's  cost  ?     How  much  did  both  cost  ? 

34.  What  is  the  cost  of  16f  yards  of  silk  at  $  2.75  a  yard  ? 

35.  What  is  the  cost  of  14|  yards  of  cambric  at  42  cents  a 
yard? 

36.  If  5J  yards  of  calico  cost  33  cents,  how  much  must  be 
paid  for  14f  yards  ? 

37.  One  yard  of  sheeting  cost  22|  cents.     How  many  yards 
can  be  bought  for  $  15.15  ? 

38.  From  a  piece  of  calico  containing  33|  yards  there  have 
been  sold  at  different  times  11J,  7|,  and  1£  yards.     How  many 
yards  remain  ? 


266       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

39.  I  bought  16  \  yards  of  cloth  for  $  3J  per  yard,  and  sold 
it  for  $  4J  per  yard.     What  was  the  gain  ? 

40.  A  merchant  has  three  pieces  of  cloth  containing,  respec- 
tively, 28|,  35  L,  and  41  f  yards.     After  selling  several  yards 
from  each  piece,  he  finds  that  he  lias  left  in  the  three  pieces 
67  yards.     How  many  yards  has  he  sold  ? 

ARITHMETIC  FOR  CASHIER 

How  to  Make  Change.  —  Every  efficient  cashier  or  saleslady 
makes  change  by  adding  to  the  amount  of  the  sale  or  purchase 
enough  change  to  make  the  sum  equal  to  amount  presented. 
The  change  should  be  returned  in  the  largest  denominations 
possible. 

To  illustrate  :  A  young  lady  buys  dry  goods  to  the  amount 
of  $  1.52.  She  gives  the  saleslady  a  $  5  bill.  What  change 
should  she  receive  ? 

The  saleslady  will  say:  $1.52,  $1.55,  -$1.65,  $1.75,  $2.00,  $4.00, 
$5.00.  That  is,  $  1.52  +  $  .03  =  $  1.65  ;  $  1.55  +  $.10  =  $  1.65  ;  $1.65 
+  $.10=  $1.75;  $1.75  +  $.25  =  $2.00;  $2.00  +  $2.00  =  $4.00  ;  $4.00 
+  $1.00  =  $5.00. 

EXAMPLES 

1.  What  change  should  be   given  for  a  dollar  bill,   if  the 
following  purchases  were  made  ? 

a.  $.87  c.   $.43  e.  $.20 

b.  $.39  d.  $.51  /.  $.23 

2.  What  change  should  be  given  for  a  two-dollar  bill,  if  the 
following  purchases  were  made  ? 

a.  $1.19  d.  $1.57  g.  $.63 

6.  $.89  e.  $1.42  h.  $.78 

c.  $1.73  /.  $1.12  i.  $.27 


ARITHMETIC    FOR   SALESGIRLS   AND    CASHIERS       267 

3.  What  change  should  be  given  for  a  five-dollar  bill,  if  the 
following  purchases  were  made  ? 

a.  $3.87  d.  $2.81  g.  $1.93 

6.   $2.53  e.  $3.74  h.  $.17 

c.   $4.19  /.   $4.29  i.  $.47 

4.  What  change  should  be  given  for  a  ten-dollar  bill,  if  the 
following  purchases  were  made  ? 

o.  $8.66  d.  $6.23  g.   $3.16 

6.  $9.31  e.  $5.29  ft.   $2.29 

c.   $7.42  /.  $4.18  t.  $1.74 

5.  What  change  should  be  given  for  a  twenty-dollar  bill,  if 
the  following  purchases  were  made  ? 

a.  $18.46  c.  $17.09  e.  $8.01 

b.  $  19.23  d.  $  12.03  /.  $  6.27 


CHAPTER   XIII 
CIVIL  SERVICE 

ALMOST  every  government  position  open  to  women  has  to  be 
obtained  through  an  examination.  In  most  cases  Arithmetic 
is  one  of  the  subjects  tested.  It  is  wise  to  know  not  only  the 
subject,  but  also  the  standards  of  marking,  and  for  this  reason 
some  general  rules  on  this  subject  follow. 

Marking  Arithmetic  —  Civil  Service  Papers 

1.  On  questions  of   addition,  where   sums  are  added  across  and  the 
totals  added,  for  each  error  deduct  16|  %. 

2.  .For  each   error  in  questions  containing  simple  multiplication  or 
division,  as  a  single  process,  deduct  50  %  ;  as  a  double  process,  deduct 
25%. 

3.  In  questions  involving  fractions  and  problems  other  than  simple 
computation,  mark  as  follows  : 

(a)  Wrong  process  leading  to  incorrect  result,  credit  0. 
(6)  For  inconvenient  or  complex  statement,  process,  or  method,  giving 
right  result,  deduct  from  5  to  25  °fc . 

(c)  If  the  answer  is  correct  but  no  work  is  shown,  credit  0. 

(d)  If  the  answer  is  correct  and  the  process  is  clearly  indicated,  but 
not  written  in  full,  deduct  25  °fo . 

(e)  If  no  attempt  is  made  to  answer,  credit  0. 

(/)  If  the  operation  is  incomplete,  credit  in  proportion  to  the  work 
done. 

(gr)  For  the  omission  of  the  dollar  sign  ($)  in  final  result  or  answer, 
deduct  5. 

(ft)  In  long  division  examples,  to  be  solved  by  decimals,  if  the  answer 
is  given  as  a  mixed  number,  deduct  25. 

4.  For  questions  on  bookkeeping  and  accounts,  mark  as  follows  : 

(a)  For  omission  of  total  heading,  deduct  25  ;  for  partial  omission,  a 
commensurate  deduction. 

(6)  For  every  misplacement  of  credits  or  debits,  deduct  25. 


CIVIL   SERVICE  269 

(c)  For  every  omission  of  date  or  item,  deduct  10. 

(d)  For  omissions  or  misplacement  of  balance,  deduct  25. 

NOTE.  —  Hard  and  fast  rules  are  not  always  applicable  because  the  impor- 
tance of  certain  mistakes  differs  with  the  type  of  example.  Before  a  set  of 
examples  is  marked,  the  deductions  to  be  made  for  various  sorts  of  errors 
are  decided  upon  by  the  examiners.  In  general,  examples  in  arithmetic  for 
high-grade  positions  are  marked  on  practically  the  same  basis  as  clerical 
arithmetic.  Arithmetic  in  lower-grade  examinations,  such  as  police  and  fire 
service  and  the  like,  is  marked  about  60%  easier  than  clerical. 

CIVIL   SERVICE  EXAMPLES 

(Give  the  work  in  full  in  each  example.) 

1.  Multiply  83,849,619  by  11,079. 

2.  Subtract  16,389,110  from  48,901,001. 

3.  Divide  18,617.03  by  .717. 

4.  At   $  0.37   per   dozen,   how   many   dozen   eggs    can  be 
bought  for  $  33.67  ? 

5.  What  would  372  pounds  of  corn  meal  cost  if  4  Ib.  cost 
12  cents  ? 

6.  If  a  man  bought  394  cows  for  $  23,640  and  sold  210 
for  $  14,700,  what  was  the  profit  on  each  cow  ? 

7.  What  is  the  net  amount  of  a  bill  for  $  93.70,  subject  to 
a  discount  of  37^-  %  ? 

8.  How  many  pints  in  a  measure  containing  14,784  cubic 
inches  ? 

9.  What  number  exceeds  the  sum  of  its  fourth,  fifth,  and 
sixth  by  23  ? 

10.  If  a  man's  yearly  income  is  $  1600,  and  he  spends  $  25 
a  week,  how  much  can  he  save  in  a  year  ? 

11.  What  will  16|-  pounds  of  butter  cost  at  34  cents  a  pound  ? 

12.  How  many  hogs  can  be  bought  for  $  1340  if  each  hog 
averages  160  pounds  and  costs  9  cents  a  pound  ? 

13.  How  many  tons  of  coal  can  be  bought  for  $446.25,  if 
each  ton  costs  $  8.75  ? 


270       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

14.  A  young  lady  can  separate  38  letters  per  minute.     If  a 
letter  averages  6^  ounces,  how  many  pounds  of  mail  does  she 
handle  in  an  hour  ? 

15.  Multiply  53 J  by  9f  and  divide    the    product    by    2^. 
(Solve  decimally.)  * 

16.  Roll  matting  costs  73 £  cents  per  sq.  yd.     What  will  be 
the  cost  of  47  rolls,  each  roll  60  yd.  long  and  36  in.  wide  ? 

17.  A  man  paid  $  5123.25  for  27  mules  and  sold  them  for 
$  6500.     How  much  did  he  gain  by  the  transaction  ? 

18.  A  wheel  measures  3'  1"  in  diameter.     What  is  the  dis- 
tance around  the  tire  ? 

19.  A  bricklayer  earns  70  cents  an  hour.     If  he  works  129 
days,  8  hours  a  day,  and  spends  $  50  a  month,  how  much  does 
he  save  a  year  ? 

20.  A  rectangular  courtyard  is  48'  5"  long  and  23'  1"  wide. 
How  many  square  yards  is  it  in  area  ? 

21.  How  many  days  will  it  take  a  ship  to  cross  the  Atlantic 
Ocean,  2970  miles,  if  the  vessel  sails  at  the  rate  of  21  miles  an 
hour  ? 

22.  Eleven  men  bought  7  tracts  of  land  with  22  acres  in 
each  tract.     How  many  acres  will  each  man  have  ? 

23.  A   merchant   sends  his   agent   $  10,228   to   buy  goods. 
What  is  the  value  of  the  goods,  after  paying  $  28  for  freight 
and  giving  the  agent  2  %  for  his  commission  ? 

24.  If  milk  costs  6  cents  a  quart,  and  you  sold  it  for  9  cents 
a  quart,  and  your  profit  for  the  milk  was  $48,  how  many 
quarts  of  milk  did  you  sell  ? 

25.  A  traveler  travels  llf  miles  a  day  for  8  days.      How 
many  more  miles  has  he  yet  to  travel  if  the  journey  is  134 
miles  ? 

26.  What  is  the  net  amount  of  a  bill  for  $29.85,  subject  to 
a  discount  of  16|  %  ? 


CIVIL   SERVICE  271 

27.  Add  across,  placing  the  totals  in  the  spaces  indicated ; 
then  add  the  totals  and  check : 

TOTALS 

8,431  17,694  18,630  91  707 

5,912               305  3,777  871  8,901 

6,801  29,006  5,891  30  16,717 

5,008  10,008  7,771  144  9,001 

13,709  10,999  39  1,113  3,444 

28.  Divide  37,818.009  by  .0391. 

29.  A  pile  of  wood  is  136  ft.  long,  8  ft.  wide,  and  6  ft.  high, 
and  is  sold  for  $  4.85  per  cord,  which  is  20  %  more  than  the 
cost.     What  is  the  cost  of  the  pile  ? 

30.  Add  the  following  column  and  from  the  sum  subtract 
81,376,019 : 

80,614,304 
68,815,519 
32,910,833 
54,489,605 
96,315,809 
75,029,034 
21,201,511 

31.  A  man  bought  128  gal.  cider  at  23  cents  a  gallon ;  he 
sold  it  for  28  cents  a  gallon.     How  much  did  he  make  ? 

32.  A  laborer  has  $48  in  the  bank.     He  is  taken  sick  and 
his  expenses  are  $  7.75  a  day.     How  many  days  will  his  fund 
last? 

33.  In   paving   a  street  If  mi.  long  and  54  ft.  wide,  how 
many  bricks  9  in.  long  and  4  in.  wide  will  be  required  ? 

34.  Find  the  simple  interest  on  $  841.37  for  2  yr.  3  mo.  17  da. 

at  5%. 

35.  Find  the  simple  interest  on  $  367.49  for  1  yr.  7  mo.  19  da. 
at  4%. 


272       VOCATIONAL  MATHEMATICS  FOR  GIRLS 

SPECIMEN   ARITHMETIC  PAPERS 

CLERKS,  MESSENGERS,  ETC. 
Rapid  Computation 

1.   Add  these  across,  placing  the  totals  in  the  spaces  in- 
dicated ;  then  add  the  totals  : 

TOTALS 


15,863 

3,175 

368 

51,461 

35,196 

27,368 

7,242 

82,463 

24,175 

52,837 

3,724 

51,493 

68,317 

58,417 

41,582 

4,738 

16,837 

5,281 

52,683 

26,364 

73,642 

25,164 

42,525 

70,463 

1,476 

18,572 

7,368 

15,726 

71,394 

62,958 

2.  Multiply  82,473,659  by  9874.  Give  the  work  in  full. 
3.  From  68,515,100  subtract  24,884,574.  Give  the  work  in 
full.  4.  Divide  29,379.7  by  .47.  Give  the  work  in  full. 

5.  What  is  the  net  amount  of  a  bill  for  $19.20,  subject  to  a 
discount  of  16f  %  ?     Give  the  work  in  full. 

Arithmetic 

1.  How  many  times  must  720  be  added  to  522  to  make 
987,642  ?  Give  the  work  in  full.  2.  If  the  shadow  of  an  up- 
right pole  9  ft.  high  is  8^  ft.  long,  what  is  the  height  of  a  church 
spire  which  casts  a  shadow  221  ft.  long  ?  Give  the  work  in  full. 
3.  How  many  sods,  each  8  in.  square,  will  be  required  to  sod  a 
yard  24  feet  long  and  10  feet  8  inches  wide  ?  Give  the  work 
in  full.  4.  A  retired  merchant  has  an  income  of  $  25  a  day, 
his  property  being  invested  at  6  % .  What  is  he  worth  ?  Give 
the  work  in  full.  5.  Find  the  principal  that  will  yield  $  38.40 
in  1  yr.  6  mo.  at  4  %  simple  interest.  Give  the  work  in  full. 

6.  If  the  time  past  noon  increased  by  90  minutes  equals  -f^ 
of  the  time  from  noon  to  midnight,  what  time  is  it  ?     Give  the 
work  in  full.     7.    A  merchant  deducts  20  %  from  the  marked 
price  of  his  goods  and  still  makes  a  profit  of  16  %.     At  what 


CIVIL   SERVICE  273 

advance  on  the  cost  are  the  goods  marked  ?  Give  the  work 
in  full.  8.  If  a  grocer  sells  a  tub  of  butter  at  22  cents  a  pound, 
he  will  gain  168  cents,  but  if  he  sells  it  at  17  cents  a  pound,  he 
will  lose  112  cents.  Find  (a)  the  weight  of  the  butter  and  (b) 
the  cost  per  pound.  Give  the  work  in  full.  9.  The  product  of 
four  factors  is  432.  Two  of  the  factors  are  3  and  4.  The  other 
two  factors  are  equal.  What  are  the  equal  factors  ?  Give  the 
work  in  full. 

STENOGRAPHER-TYPEWRITER 

1.  From  what  number  can  857  be  subtracted  307  times  and 
leave  a  remainder  of  49  ?     Give  the  work  in  full. 

2.  What  number  exceeds  the  sum  of  its  fourth,  fifth,  sixth, 
and  seventh  parts  by  101  ?     Give  the  work  in  full. 

3.  A  sells  to  B  at  10'%  profit;  B  sells  to  C  at  5  %  profit; 
if  C  paid  $  5336.10,  what  did  the  goods  cost  A  ?     Give  the 
work  in  full. 

4.  Find  the  simple  interest  of  $  297.60  for  3  yr.  1  mo.  15  da. 
at  6  %.     Give  the  work  in  full. 

5.  A  man  sold  \  of  his  farm  to  B,  f  of  the  remainder  to  C, 
and  the  remaining  60  acres  to  D.      How  many  acres  were  in 
the  farm  at  first  ?     Give  the  work  in  full. 

SEALERS  OF  WEIGHTS  AND  MEASURES 
(Review  Weights  and  Measures,  pages  43,  276) 

1.  A  measure  under  test  is  found  to  have  a  capacity  of 
332.0625  cu.  in.     What  is  its  capacity  in  gallons,  quarts,  etc.  ? 
Give  the  work  in  full. 

2.  How  many  quarts,  dry  measure,  would  the  above  meas- 
ure hold  ?     Give  the  work  in  full,  carrying  the  answer  to  four 
decimal  places. 

3.  What  is  the  equivalent  of  175  Ib.  troy  in  pounds  avoir- 
dupois ?     Give  the  work  in  full.     1  av.  Ib.  =  7000  grains.- 


274        VOCATIONAL   MATHEMATICS   FOR   GIRLS 

4.  How  many  grains  in  12  Ib.  15  oz.  avoirdupois  ?     Give 
the  work  in  full. 

5.  Reduce  15  Ib.  10  oz.  20  grains  avoirdupois    to  grains 
troy  weight.     Give  the  work  in  full. 

6.  What  part  of  a  bushel  is  2  pecks  and  3  pints  ?     Give 
the  work  in  full  and  "the  answer  both  as  a  decimal  and  as  a 
common  fraction. 

7.  What  will  10  bushels  3  pecks  and  4  quarts  of  seed  cost 
at  $  2.10  per  bushel  ?     Give  the  work  in  full. 

8.  What  part  of  a  troy  pound  is  50  grains,  expressed  both 
decimally  and  in  the  form  of  a  common  fraction  ? 

9.  A  strawberry  basket  was  found  to  be  65.2  cubic  inches 
in   capacity.      (a)    How   many   cubic    inches   short   was   it  ? 
(&)  WThat  percentage  of  a  full  quart  did  it  contain  ?     Give  the 
work  in  full. 

10.  In  testing  a  spring  scale  it  was  found  that  in  weighing 
22  Ib.  of  correct  test  weights  on  same,  the  scale  indicated 
22  Ib.  101  oz.  What  was  the  percentage  of  error  in  this  scale 
at  this  weight  ?  Give  the  work  in  full. 

VISITOR 

1.  A  certain  "home"  had  at  the  beginning  of  the  year 
$  693.07,  and  received  during  the  year  donations  amounting 
to    $  1322.48.     The    expenses    for    the   year   were :    salaries, 
$387.25  ;  printing,  etc.,  $175  ;  supplies,  $651.15  ;  rent,  $104.25 
heat,  etc.,  $  75  ;  interest,  $  100  ;  miscellaneous,  $  72.83.     Find 
the  cash  on  hand  at  the  end  of  the  year.     Give  the  work  in 
full. 

2.  Of  the  72,700  persons  relieved  in  a  certain  state  at  public 
expense  in  the  year  ending  March  31,  1912,  76  %  were  aided 
locally,  and  the  remainder  by  the  state.      Find    the  number 
relieved  by  the  state.     Give  the  work  in  full. 


CIVIL   SERVICE  275 

3.  There  was  spent  in  state,  city,  and  town  public  poor  relief 
in  Massachusetts  in  one  year  the  sum  of  $3,539,036.      The 
number  of  beneficiaries  was  72,700.     What  was   the  average 
sum  spent  per  person  ?     Give  the  work  in  full. 

4.  Of  the  72,900  persons  aided  by  public  charity  in   this 
state  in  a  certain  year  y9-^  were  classed  as  sane.     Of  the  re- 
mainder, ±  were  classed  as  insane,  ^  as  idiotic,  and  the  rest  as 
epileptic.     How  many  epileptics  received  public  aid?     Give, 
the  work  in  full. 


PART  V  — ARITHMETIC   FOR   NURSES 

CHAPTER   XIV 

A  NURSE  should  be  familiar  with  the  weights  and  measures 
used  in  dispensing  medicines.  There  are  two  systems  used  — 
the  English,  based  on  the  grain,  and  the  Metric  system,  based 
on  the  meter. 

APOTHECARIES'  WEIGHT 
(Troy  Weight) 

20  grains  (gr.)  =  1  scruple  (3) 

33  =1  dram  (  3  )  =  60  gr. 

83  =1  ounce  (  3  )  =  24  3  =480  gr. 

123  =1  pound  (ft)  =96  3  =288  3  =  5760  gr. 

The  number  of  units  is  often  expressed  by  Roman  numerals 
written  after  the  symbols.  (See  Roman  Numerals,  p.  2.) 

EXAMPLES 

1.  How  many  grains  in  iv  scruples  ? 

2.  How  many  grains  in  iii  drams  ? 

3.  How  many  grains  in  iv  ounces  ? 

4.  How  many  scruples  in  lb  i  ? 

5.  How  many  grains  in  lb  iii  ? 

6.  How  many  drams  in  lb  iv  ? 

7.  How  many  grains  in  3  ii  ? 

8.  How  many  scruples  in  3  v  ? 

9.  How  many  drams  in  5  vii  ? 

10.    How  many  ounces  in  lb  viii  ? 

276 


ARITHMETIC   FOR   NURSES  277 

11.  Salt  5  i  will  make  how  many  quarts  of  saline  solution, 
gr.  xc  to  qt.  1  ? 

12.  How  many  drains  of  sodium  carbonate  in  10  powders  of 
Seidlitz  Powder  ?     Each  powder  contains  gr.  xl. 

APOTHECARIES'  FLUID  MEASURE 

60  minims  (m)  =  1  fluid  dram  =  (f  3  ). 

8  f  3  =1  fluid  ounce  (f  3). 

16  f  3  =1  pint  (0)  =  128  f  3  =  7680  m. 

8  O  =1  gallon  (C)  =  128  f  3  =1024  f  3 . 

EXAMPLES 

1.  How  many  minims  in  f  3  iv  ? 

2.  How  many  minims  in  f  3  iii  ? 

3.  How  many  fluid  drams  in  1  0  ? 

4.  How  many  minims  in  5  pints  ? 

5.  How  many  pints  in  8  gallons  ? 

6.  How  many  fluid  drams  in  0  ii  ? 

7.  How  many  minims  in  f  5  viii  ? 

8.  How  many  fluid  drams  in  C  vii  ? 

9.  How  many  pints  in  C  v  ? 

10.  How  many  minims  in  f  5  ix  ? 

11.  If  the  dose  of  a  solution  is  m  xxx  and  each  dose  contains 
-^g-  gr.  strychnine,  how  much  of  the  drug  is  contained  in  f  5  i 
of  the  solution  ? 

12.  3  ii  of  a  solution  contains  gr.  i  of  cocaine.     How  much 
cocaine  is  given  when  a  doctor  orders  m  x  of  the  solution  ? 

Approximate  Measures  of  Fluids 

(With  Household  Measures) 

An  ordinary  teaspoonful  is  supposed  to  hold  60  minims  of 
pure  water  and  is  approximately  equal  to  a  fluid  dram.     A 


278       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


A  GRADUATE. 


drop  is  ordinarily  considered  equivalent 
to  a  minim,  but  this  is  only  approxi- 
mately true  in  the  case  of  water.  The 
specific  gravity,  shape,  and  surface  from 
which  the  drop  is  poured  influence  the 
size.  In  preparing  medicines  to  be 
taken  internally,  minims  should  never 
be  measured  out  as  drops.  There  are 
minim  droppers  and  measures  for  this 
purpose. 

A  level  teaspoonful  of  either  a  fluid 
or  solid  preparation  is  equal  to  a  dram. 
Level  spoonfuls  are  always  considered 
in  measurements. 


1  teaspoonful         =  1  fluid  dram. 

1  dessertspoonful  =  2  fluid  drains. 

1  tablespoonful      =  4  fluid  drams  or  J  fluid  ounce. 

1  wineglassf  ul       =  2  fluid  ounces. 

1  teacupful  =  6  fluid  ounces. 

1  tumblerful          =  8  fluid  ounces. 

EXAMPLES 

1.  How  many  dessertspoonfuls  in  8  fluid  ounces  ? 

2.  How  many  wineglassfuls  in  2  tumblerfuls  ? 

3.  How  many  tablespoonfuls  in  3  fluid  drams  ? 

4.  How  many  teaspoonful  s  in  5  fluid  ounces  ? 

5.  How  many  teacupfuls  in  4  fluid  drams  ? 

6.  How  many  dessertspoonfuls  in  6  fluid  drams  ? 

7.  How  many  teaspoonfuls  in  1  gallon  ? 

8.  How  many  drops  of  water  in  1  quart  ? 

9.  How  many  teaspoonfuls  in  3  ounces  ? 
10.  How  many  minims  in  3  pints  ? 


ARITHMETIC   FOR   NURSES  279 

11.  What  household  measure  would  you  use  to  make  a  solu- 
tion, 3  i  to  a  pint  ? 

12.  Read  the  following  apothecaries'  measurements  and  give 
their  equivalents : 

a.  3  iv.  /.  3  ss.1 

b.  gr.  v.  g.  0  iv. 

c.  0  ii.  h.  3  ii. 

d.  5  ii-  *"•  3  iv. 

e.  §  ij.  j.  I  ss. 

Metric  System  of  Weights  and  Measures 

(Review  Metric  System  in  Appendix.) 

The  metric  system  of  weights  and  measures  is  used  to  a 
great  extent  in  medicine.  The  advantage  of  this  system  over 
the  English  is  that,  in  preparing  solutions,  it  is  easy  to  change 
weights  to  volumes  and  volumes  to  weights  without  the  use  of 
common  fractions. 

In  medicine  the  gramme  (so  written  in  prescriptions  to 
avoid  confusion  with  the  dram)  and  the  milligramme  are  the 
chief  weights  used. 

1  gramme  =  wt.  of  1  cubic  centimeter  (cc. )  of  water  at  4°  c. 

1000  grammes  =  1  kilogram  or  "  kilo." 

1  kilogram  of  water  =  1000  cc.  =  1  liter. 

CONVERSION  FACTORS 

1  gramme  =  15.4  or  approx.  15  grains. 

1  grain  =  0.064  gramme. 

1  cubic  centimeter  =  15  minims. 

1  minim  =  0.06  cc. 

1  liter  =  1  quart  (approx.). 

The  liter  and  cubic  centimeter  are  the  principal  units  of 
volume  used  in  medicine. 

1  ss  means  one-half. 


280       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

A  micro-millimeter  is  used  in  measuring  microscopical  dis- 
tances.    It  is  r^  mm.  and  is  indicated  by  the  Greek  letter  /A. 

To  convert  cc.  into  minims  multiply  by  15. 
To  convert  grammes  into  drams  divide  by  4. 
To  convert  cc.  into  ounces  divide  by  30. 
To  convert  minims  into  cc.  divide  by  15. 
To  convert  grains  into  grammes  divide  by  15. 
To  convert  fluid  drams  into  cc.  multiply  by  4. 
To  convert  drams  into  grammes  multiply  by  4. 

1  grain  =  0.064  gramme. 

2  grains  =  0.1  gramme. 
5  grains  =  0.3  gramme. 
8  grains  =  0.5  gramme. 

10  grains  =  0.6  gramme. 

15  grains  =  1  gramme. 

1  milligramme  =  0.0154  grain. 

Review  Troy  (apothecary)  and  avoirdupois  weights,  pages 
43  and  276. 

EXAMPLES 

1.  A  red  corpuscle  is  8  /x,  in  diameter.     Give  the  diameter  in 
a  fraction  of  an  inch. 

2.  A  microbe  is  25000"  inch  in  diameter.     What  part  of  a 
millimeter  is  it  ? 


3.  Another  form  of  microbe  is  -Q^-^Q  of  an  inch  in  diameter. 
What  part  of  a  millimeter  is  it  ? 

4.  A  bottle  holds  48  cc.     What  is  the  weight  of  water  in  the 
bottle  when  it  is  filled  ? 

5.  How    many  liters  of  water  in  a  vessel  containing  4831 
grams  of  water  ? 

6.  Give   the    approximate    equivalent    in    English    of    the 
following  : 

a.  48  grammes  d.   8  kilos 

b.  3.6  kilograms  e.   3:9  grammes 

c.  3.5  liters  /.    53  milligrammes 


ARITHMETIC   FOR   NURSES  281 

7.    Give  the  approximate  equivalents  in  the  metric  system 
of  the  following : 

a.  39  grains  e.   13  quarts 

b.  4  drams  /.   2  gallons 

c.  1  fluid  drams  g.   39  minims 

d.  47  flb  h.    8321  grains 

Approximate  Equivalents  between  Metric  and  Household 

Measures 

1  teaspoon ful        =      4  cc.  or  4  grams  of  water. 
1  dessertspoonful  =     8  cc.  or  8  grams  of  water. 
1  tablespoonful     =    16+  cc.  or  15+  grams  of  water. 
1  wineglassful        =    60  cc.  or  60  grams  of  water. 
1  teacupful  =  180  cc.  or  180  grams  of  water. 

1  glassful  =  240  cc.  or  240  grams  of  water. 

EXAMPLES 

(Give  approximate  answers.) 

1.  What  is  the  weight  of  two  glassfuls  of  water  in  the 
metric  system  ? 

2.  What  is  the  weight  of  a  gallon  of  water  in  the  metric 
system  ? 

3.  What  is  the  weight   of   three   liters   of   water   in   the 
English  system  ? 

4.  What  is  the  volume  of   four   ounces  of  water  in   the 
metric  system  ? 

5.  What  is  the  volume  of  twelve  cubic  centimeters  of  water 
in  the  English  system  ? 

6.  What  is  the  volume  of  f  3  iii  in  the  metric  system  ? 

7.  What  is  the  volume  of  eighty  grammes  of  water  ? 

8.  What  is  the  weight  of  360.1  cc.  of  water  ? 

9.  What  is  the  volume  of  4  kilos  of  water  ? 

10.  What  is  the  weight  of  6.1  liters  of  water  ? 

11.  With    ordinary    household   measures    how    would   you 
obtain  the  following :  5  gm.,  m  xv,  1.5  L.,  25  cc.,  5  ii,  f  5  ss  ? 


282       VOCATIONAL   MATHEMATICS   FOR   GIRLS 
METRIC  SYSTEM 

EXAMPLES 

1.  Change  the  following  to  milligrammes  : 
8  gin.,  17  dg.,  13  gm. 

2.  Change  the  following  to  grammes  : 
13  mg.,  29  dg.,  7  dg.,  21  mg. 

3.  Add  the  following  : 

11  mg.,  18  dg.,  21  gm.,  4.2  gm. 

Express  answer  in  grammes. 

4.  Add  the  following  : 

25  mg.,  1.7  gm.,  9.8  dg.,  21  mg. 

Express  answer  in  milligrammes. 

5.  The  dose  of  atropine   is   0.4  mg.     What  fraction  of  a 
gramme  is  necessary  to  make  25  cc.  of  a  solution  in  which  1  cc. 
contains  the  dose  ? 

6.  Give  the  equivalent  in  the  metric  system  of  the  following 
doses : 

a.  Extract  of  gentian,  gr.  ^. 

b.  Tincture  of  quassia,  3  i. 

c.  Tincture  of  capsicum,  m  iii. 

d.  Spirits  of  peppermint,  3  i. 

e.  Cinnamon  spirit,  m  x. 
/.  Oil  of  cajuput,  m  xv. 

g.   Extract  of  cascara  sagrada,  gr.  v. 
h.   Fluid  extract  of  senna,  3  ii. 
i.    Agar  agar,  5  ss. 

7.  Give  the  equivalent  in  the  English  system  of  the  follow- 
ing doses : 

a.   Ether,  1  cc. 

6.    Syrup  of  ipecac,  4  cc. 

c.    Compound  syrup  of  hypophosphites,  4  cc. 


ARITHMETIC   FOR   NURSES  283 

d.  Pancreatin,  0.3  gm. 

e.  Zinc  sulphate,  2  gm. 

/.  Copper  sulphate,  0.2  gm. 

g.  Castor  oil,  30  cc. 

h.  Extract  of  rhubarb,  0.6  gm. 

i.  Purified  aloes,  0.5  gm. 

DOSES 

Since  all  drugs  are  harmful  or  poisonous  in  sufficiently  large 
quantities,  it  is  necessary  to  know  the  least  amount  needed  to 
produce  the  desired  change  in  the  body  —  the  minimum  dose. 
This  has  been  ascertained  by  careful  and  prolonged  experiments. 
Similar  experiments  have  told  us  the  largest  amount  of  drug 
that  one  can  take  without  producing  dangerous  effect  —  the 
maximum  dose. 

On  the  average,  children  under  12  years  of  age  require  smaller 
doses  than  adults.  To  determine  the  fraction  of  an  adult  dose 
of  a  drug  to  give  to  a  child,  let  the  child's  age  be  the  numer- 
ator, and  the  sum  of  the  child's  age  plus  twelve  be  the  denomina- 
tor of  the  fraction.  For  infants  under  one  year,  multiply  the 

adult  dose  by  the  fraction  ^  in  months  _ 

lou 

To  illustrate :  How  much  of  a  dose  should  be  given  to  a 
child  of  four  ? 

Age  of  child  =  4. 

Age  of  child  +  12  =  16. 

Fraction  of  dose  T\  =  \,     Ans.  £  of  a  dose. 

EXAMPLES 

1.  What  is  the  fraction  of  a  dose  to  give  to  a  child  of  8  ? 

2.  What  is  the  fraction  of  a  dose  to  give  to  a  child  of  6  ? 

3.  What  is  the  fraction  of  a  dose  to  give  to  a  child  of  3  ? 

4.  What  is  the  fraction  of  a  dose  to  give  to  a  child  of  10  ? 


284       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

5.  If  the  normal  adult  dose  of  aromatic  spirits  of  ammonia 
is  1  dram,  what  is  the  dose  for  a  child  of  7  ? 

6.  If  the  normal  adult  dose  of  castor  oil  is  one-half  ounce, 
what  is  the  dose  for  a  child  of  6  ? 

7.  If  the  normal  adult  dose  of  epsom  salts  is  4  drams, 
what  is  the  dose  for  a  child  of  4  ? 

8.  If  the  normal  adult  dose  of  strychnine  sulphate  is  ^  gr., 
what  is  the  dose  for  a  child  of  8  ? 

9.  If  the  normal  adult  dose  of  ipecac  is  15  grains,  what  is 
the  dose  for  a  child  of  11  ? 

10.  If  the  normal  adult  dose  of  aromatic  spirits  of  ammonia 
is  4  grammes,  what  is  the  dose  for  a  child  of  5  m'onths  ? 

11.  If  the  normal  adult  dose  of  ipecac  is  1  gramme,  what  is 
the  dose  for  a  child  10  months  old  ? 

12.  The  normal  adult  dose  of  strychnine  sulphate  is  3.2  mg. 
How  much  should  be  given  to  a  child  2  years  old  ? 

STRENGTH  OF  SOLUTIONS 

A  nurse  should  know  about  the  strength  of  substances  used 
in  treating  the  sick.  Most  of  these  substances  are  drugs  which 
are  prepared  according  to  formulas  given  in  a  book  called  a 
Pharmacopoeia.  Preparations  made  according  to  this  standard 
are  called  official  preparations,  and  often  have  the  letters 
U.  S.  P.  written  after  them  to  distinguish  them  from  patented 
preparations  prepared  from  unknown  formulas. 

Drugs  are  applied  in  the  following  forms :  solutions,  lini- 
ments, oleates,  cerates,  powders,  lozenges,  plasters,  ointments, 
etc. 

An  infusion  is  a  liquid  preparation  of  the  drug  made  by 
extracting  the  drug  with  boiling  water.  The  strength  of  an 
infusion  is  5%  of  the  drug,  unless  otherwise  ordered  by  the 
physician. 


ARITHMETIC   FOR   NURSES  285 

The  strength  of  a  solution  may  be  written  as  per  cent  or  in 
the  form  of  a  ratio.  A  10  %  solution  means  that  in  every 
100  parts  by  weight  of  water  or  the  solvent  there  are  10  parts 
by  weight  of  the  substance.  This  may  be  written  in  form 
of  a  fraction  —  y1^-  or  y1^-.  In  other  words,  for  every  ten  parts 
of  solvent  there  is  one  part  of  substance.  Since  a  fraction  may 
be  written  as  a  ratio,  it  may  be  called  a  solution  of  one  to  ten, 
written  thus,  1 : 10. 

EXAMPLES 

1.  Express  the  following  per  cents  as  ratios:   5%,  20%, 
2%,  0.1%,  0.01%. 

Since  per  cent  represents  so  many  parts  per  hundred,  a 
ratio  may  be  changed  to  per  cent  by  putting  it  in  the  form 
of  a  fraction  and  multiplying  by  100.  The  quotient  is  the  per 
cent. 

2.  Express    the   following   in   per   cents  :    1  : 4,  1 :  3,  1  :  6, 
1  : 15,  1 :  25,  1  :  40. 

3.  Arrange   the  following  solutions  in  the  order  of   their 
strength  :    3  %,  8  %,  24  %,  6  %,  1 : 10,  1 : 14, 1  :  50,  40  %,  1 :  45, 
50%. 

4.  Express  the  strength  of  the  following  solutions  as  per 
cents,  and  in  ratios. 

a.  80  ounces  of  dilute  alcohol  contains  40  ounces  of  absolute 
alcohol. 

6.  6  pints  of  dilute  alcohol  contains  two  pints  of  absolute 
alcohol. 

5.  Change  the  following  ratios  into  per  cents  :  1  : 18,  1  :  20, 
1:5,     1  :  35,     1 : 100.      Arrange  in  order,  beginning  with  the 
highest. 

6.  Change  the  following  per  cents  to  ratios :    33  % ,  12  % , 
15%,  .5%,!%. 

7.  Is  it  possible  to  make  an  8  %  solution  from  4  %  ?     Ex- 
plain. 


286       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

8.  Express  the  following  strengths  in  terms  of  ratio : 

a.  25  cc.  of  alcohol  in  100  cc.  solution. 

b.  5  pints  of  alcohol  in  3  qts. 

c.  f  §  i  contains  f  3  iii. 

9.  Express  the  following  strengths  in  terms  of  per  cent : 

a.  50  cc.  of  ^solution  containing  5  cc.  of  peroxide  of  hydrogen. 

b.  f  5  iii  of  dilute  alcohol  containing  ^  ii  of  pure  alcohol. 

How  to  Make  Solutions  of  Different  Strengths  from  Crude 
Drugs  or  Tablets  of  Known  Strengths 

Exact  Method 

ILLUSTRATIVE  EXAMPLE.  —  How  much  water  will  be  neces- 
sary to  dissolve  5  gr.  of  powdered  bichloride  of  mercury  to 
make  a  solution  of  1  part  to  2000  ? 

Since  the  whole  powder  is  dissolved, 

1  part  is  5  gr. 

2000  parts  =  10,000  grains. 
480  gr.  =  1  oz. 
32  oz.  =  1  qt. 

10000  _  20f .  Approx.  21  oz.  or  1£  pints  of  water  should  be  used  to 
dissolve  it. 

The  above  example  may  be  solved  by  proportion,  when  x  =  no.  oz.  of 
water  necessary  to  dissolve  powder  ;  then  wt.  of  powder  :  drug  :  :  x  :  water. 

f  „  :  1  :  :  X  :  2000. 

>  =  20|oZ.    Approx.  21o, 


EXAMPLES 

Solve  the  following  examples  by  analysis  and  proportion : 

1.  How  much  water  will  be  required  to  dissolve  5  gr.  of 
powdered  corrosive  sublimate  to  make  a  solution  of  1  part  to 
1000? 


ARITHMETIC   FOR   NURSES  287 

2.  How  much  water  will  be  required  to  dissolve  a  7^-grain 
tablet  of  corrosive  sublimate  to  make  a  solution  1  part  to  2000  ? 

ILLUSTRATIVE  EXAMPLE.  —  How  much  of  a  40  %  solution 
of  formaldehyde  should  be  used  to  make  a  pint  of  1  :  500 
solution  ? 

480  minims  =  1  oz. 
7680  minims  =  1  pint. 


=  15295  minims  =  amt.  of  pure  formaldehyde  necessary  to  make  a 
pint  of  1  :  500. 

Since  the  strength  of  the  solution  is  40%,  15^  minims  represents  but 
A°o  or  f  °f  the  actual  amount  necessary.  Therefore,  the  full  amount  of 
40  °/o  solution  is  obtained  by  dividing  by  f  . 

192 

?j*  x  I  =  —  =  38§  minims  to  a  pint. 


To  Determine  the  Amount  of  Crude  Drug  Necessary  to  Make  a 
Certain  Quantity  of  a  Solution  of  a  Given  Strength 

To  illustrate  :    To  make  a  gallon  of  1  :  20  carbolic  acid  solu- 
tion, how  much  crude  carbolic  acid  is  necessary  ? 

1  :  20  :  :  x  :  1  gal. 
1  :  20  :  :  x  :  8  pints  or  128  ounces. 
20  x  =  128  ounces. 

x  =  6f  ounces  crude  carbolic  acid. 

EXAMPLES 

1.  How  much  crude  boric  acid  is  necessary  to  make  6  pints 
of  5  %  boric  acid  ? 

5  :  100  :  :  x  :  6  pts. 

6  :  100  :  :  x  :  576  drams. 
100  x  =  2880. 

x  -  28.8  drams. 

2.  How  much  crude  boric  acid  is  necessary  to  make  2  quarts 
of  1  :  18  boric  acid  ? 


288       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

3.  How  much  crude  drug  is  necessary  to  make  f  3iii  of  2  % 
cocaine  ? 

4.  How  many  7J~grain  tablets  are  necessary  to  make  2  gal- 
lons of  1 : 1000  bichloride  of  mercury  ?  1 

5.  How  much  crude  drug  is  necessary  to  make  0  vi  of  1 :  20 
phenol  solution  ? 

6.  How  much  crude  drug  is  necessary  to  make  0  vii  of  1  :  500 
bichloride  of  mercury  ? 

7.  How  much  crude  drug  is  necessary  to  make  0  iii  of  1  : 10 
chlorinated  lime  ? 

Hypodermic  Doses 

Standard  strong  solutions  and  pills  are  kept  on  hand  in  a 
hospital  and  from  these  weaker  solutions  are  made  as  required 
by  the  nurse  for  hypodermic  use.  This  is  done  by  finding  out 
what  part  the  required  dose  is  of  the  tablet  or  solution  on 
hand.  The  hypodermic  dose  is  not  administered  in  more  than 
25  or  less  than  10  minims.  The  standard  pill  or  solution  is 
dissolved  or  diluted  in  about  20  minims  and  the  fractional 
part,  corresponding  to  the  dose,  is  used  for  injection. 

To  illustrate :  A  nurse  is  asked  to  give  a  patient  -^ir  gr. 
strychnine.  She  finds  that  the  only  tablet  on  hand  is  -£$  gr. 
How  will  she  give  the  required  dose  ? 

•dro  -s-  sV  =  imr  x  30  =  -^ 

The  required  dose  is  ^  of  the  stock  pill.  Therefore  she  dissolves  the 
pill  in  80  minims  of  water  and  administers  12  minims.  The  reason  for 
dissolving  in  80  rather  than  in  20  minims  is  to  have  the  hypodermic 
dose  not  less  than  10  minims. 

EXAMPLES 

1.  Express  the  dose,  in  the  illustrative  example,  in  the 
metric  system. 

1  Hospitals  usually  use  1  tablet  for  a  pint  of  water  to  make  1  : 1000  solution. 


ARITHMETIC   FOR   NURSES  289 

2.  How  would  you  give  a  dose  g-1^  gr.  strychnine  sulphate 
from  stock  tablet  -^  gr.  ? 

3.  How  would  you  give  gr.  -J^,  if  only  -^  grain  were  on 
hand? 

4.  How  would  you  give  gr.  y1^,  if  only  ^--grain  tablets  were 
on  hand  ? 

5.  How  would  you  give  gr.  -£$,  if  only  ^y-grain  tablets  were 
on  hand  ? 

6.  How  would  you  give  gr.  g-1^,  if  only  T^7-grain  tablets  were 
on  hand  ? 

7.  How  would  you  give  gr.  y^  of  atropine  sulphate,  if  only 

in  tablets  were  on  hand  ? 


8.  How  would  you  give  gr.  -^  of  apomorphine  hydrochloride 
if  only  y^grain  tablets  were  on  hand  ? 

To  Estimate  a  Dose  of  a  Different  Fractional  Part  of  a  Grain 
from  the  Prepared  Solution 

Nurses  are  often  required  to  give  a  dose  of  medicine  of  a 
different  fractional  part  of  a  grain  from  the  drug  they  have. 

To  illustrate  :  Give  a  dose  of  -^  gr.  of  strychnine  when  the 
only  solution  on  hand  is  one  containing  -fa  gr.  in  every  10 
minims. 

Since  ^  grain  is  contained  in  10  minims, 
1  grain  or  30  x  -^  grain  is  contained  in  300  minims. 
Then,  ^  of  a  grain  is  ^  of  300  =  ^  x  300  =  12  m. 

EXAMPLES 

1.  What  dose  of  a  solution  of  60  minims  containing  -^  gr. 
will  be  given  to  get  T^  gr.  ? 

2.  Reckon  quickly  and  accurately  how  much   of   a  tablet 
gr.  i  should  be  given  to  have  the  patient  obtain  a  dose  gr.  y1^. 


290       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

3.  What  dose  of  a  solution  of  in  x  containing  gr.  i  morphine 
sulphate  will  be  given  to  give  gr.  1  ? 

4.  What  dose  of  a  solution  of  m  xx  containing  gr.  -^  strych- 
nine sulphate  will  be  given  to  give  gr.  -fa  ? 

5.  What  dose  of  a  solution  of  1  cc.  containing  0.1  cc.  of  the 
fluid  extract  of  nux  vomica  will  be  given  to  give  0.06  cc.  ? 

To  Obtain  a  Definite  Dose  from  a  Stock  Solution 
of  Definite  Strength 

To  illustrate :  To  give  a  patient  a  yL-grain  dose  when  the 
stock  solution  has  a  strength  of  1%. 

1  °IG  solution  means  that  each  drop  of  the  solution  contains  T^7  part  or 

— ££-'  of  strychnine. 
100 

2*5  gr.  is  contained  in  as  many  drops  as  T^  is  contained  in  it. 

A  *  T*<T  =  h  x  100  =  4. 
Therefore  4  drops  of  the  1  °fo  solution  contains  "^  gr. 

EXAMPLES 

1.  To  give  fa  gr.  strychnine  from  2  %  solution. 

2.  To  give    2T  gr.  strychnine   from  solution  containing  in 
ten  minims  ^  gr. 

3.  To  give  3  gr.  of  caffeinic  sodium  benzoate  from  a  25  % 
solution. 

4.  To  give  2-J-Q-  gr.  of  atropine  from  1  %  solution. 

5.  To  give  Y^-Q  gr.  of  strychnine  from  l  °/0  solution. 

6.  To  give  ^  gr.  atropine  from  solution  containing  in  ten 
minims  -^  gr. 


ARITHMETIC    FOR   NURSES  291 

Temperature 

The  temperature  of  the  body  is  due  to  the  combined  activity 
of  all  its  various  systems  but  is  regulated  chiefly  by  the  skin  and 
circulatory  system.  It  remains  very  nearly  constant  in  the  nor- 
mal person,  in  spite  of  the  variations  of  the  outdoor  temperature. 
A  variation  of  more  than  one  degree  from  the  normal  tempera- 
ture, that  is,  above  991°  F.  or  below  971°  F.,  may  be  regarded  as 
a  sign  of  a  disease.  The  temperature  is  obtained 
by  means  of  a  small  thermometer —  called  a  clinical 
thermometer.  See  Appendix,  page  337,  for  descrip- 
tion of  the  different  thermometers. 

Temperature  readings  are  usually  expressed  in 
the  Fahrenheit  scale,  but  scientific  data  gathered 
in  laboratories  are  expressed  according  to  the  Centi- 
grade scale.  Therefore,  we  should  be  able  to  change 
readings  from  one  scale  to  another. 

Fahrenheit  readings  may  be  obtained  by  adding 
32°  to  f  of  the  Centigrade  reading.     This  rule  may      ' 
be  abbreviated  into  a  formula  as  follows  : 

^=1(7+32°, 

where  F  =  Fahrenheit  reading, 
C  —  Centigrade  reading. 

Centigrade  readings  may  be  obtained  by  sub 
tracting  32°  from  the  Fahrenheit  and  taking  -|  of 
the  remainder.  This  may  be  abbreviated  into  a 
formula  as  follows  :  CLINICAL 

THBRMOM- 

320. 


EXAMPLES 

1.   Albumin  is  coagulated  by  heat  at  155°  F.     What  is  the 
degree  Centigrade  ? 


292       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

2.  When  milk  is  heated  above  170°  F.,  the  albumin  coagulates 
and  forms  a  scum  on  the  milk.     To  what  degree  on  Centigrade 
scale  does  this  correspond  ? 

3.  Egg  albumin  (white  of  egg)  coagulates  at  138°  F.     At 
what  degree  on  the  Centigrade  scale  ? 

4.  Milk  is  pasteurized  by  bringing  milk  in  the  bottle  to  a 
temperature  of  165°  F.     To  what  degree  on  the  Centigrade 
scale  ? 

5.  "  Gentle  heat "  is  a  term  used  to  denote  the  temperature 
between  32°  to  38°  C.     What  are  the  corresponding  degrees  on 
the  Fahrenheit  scale  ? 

Baths 

(Change  the  following  temperatures  to  Centigrade  scale.) 

A  bath  with  a  temperature  between  33°  and  65°  F.  is  known 
as  a  cold  bath. 

A  bath  with  a  temperature  between  65°  and  75°  F.  is  known 
as  a  cool  bath. 

A  bath  with  a  temperature  between  75°  and  85°  F.  is  known 
as  a  temperate  bath. 

A  bath  with  a  temperature  between  85°  and  92°  F.  is  known 
as  a  tepid  bath. 

A  bath  with  a  temperature  between  92°  and  98°  F.  is  known 
as  a  warm  bath. 

A  bath  with  a  temperature  between  98°  and  112°  F.  is  known 

as  a  hot  bath. 

i 

Medical  Chart  (Graph) 

(See  Graphs  in  the  Appendix.) 

In  order  to  follow  the  condition  of  a  patient  from  day  to 
day,  the  temperature,  the  pulse  beats,  and  respirations  are 
recorded  morning  and  night  on  a  special  ruled  chart.  The 
name  of  the  patient  is  placed  on  each  chart. 


ARITHMETIC    FOR   NURSES 


293 


NAME..... 


Day  of 
Month 
HoMf 


101' 


i=t 


I     I 


!    I 


TT 


294       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


EXAMPLES 

Chart  the  following  case  of  pneumonia : 


2  day 

3  day 

4  day 

5  day 

6  day 

7  day 

8  day 

9  day 

10  day 

11  day 

12  day 

13  day 

14  day 


Morning 

102° 

102.6° 

102.4° 

102.4° 

102.4° 

102.4° 

101.8° 

102.9° 

102° 

98.4° 

97.4° 

97.4° 

98.2° 


Evening 
104° 
105° 
104.2° 
103.6° 
104° 
104.4° 
103° 
104° 
102.8° 
98.5° 
98.2° 
98.2° 
98.4° 


PROBLEMS  IN   HOUSEHOLD  CHEMISTRY 

Bacteria  are  low  forms  of  vegetable  and  animal  life,  and  some 
are  capable  of  producing  disease. 

Chemicals  that  are  employed  to  destroy  bacteria  are  known 
as  germicides.  Those  which  limit  the  growth  or  destructive 
power  of  bacteria  are  called  antiseptics.  Deodorants  remove  or 
neutralize  unpleasant  odors. 

1.  Bacteria  multiply  in   all  temperatures   between  2°  and 
70°  C.     What  are   the  temperatures  in  the  Fahrenheit  scale 
within  which  bacteria  will  grow  ? 

2.  Creolin  is  used  as  a  germicide  and  deodorant  for  offen- 
sive wounds  in  solutions  of  from  2  to  5  °/0.     The  creolin  must 
never  be  added  to  water  over  98°  C.,  as  its  strength  is  impaired. 
What   is   the  corresponding  temperature  on   the   Fahrenheit 
scale  ? 

3.  The  most  important  medium  or  preparation  for  growing 
bacteria  is  nutrient  bouillon.     It  is  made  of  the  following : 


ARITHMETIC   FOR   NURSES  295 

Meat  extract  5  grams 

Peptone  10  grams 

Salt  5  grams 

Water  1  liter 

What  per  cent  of  each  ? 

4.  A  sugar  bouillon  culture  is  used  for  artificially  cultivat- 
ing bacteria.     It  is  made  by  adding  1  %  of  glucose  to  nutrient 
bouillon.     How  many  grams  of  glucose  to  a  liter  of  solution? 

5.  Carbolic  acid  is  bought  by  hospitals  in  a  95  %  solution 
and  diluted  as  required.     A  solution  of  carbolic  acid  1  : 20  is 
used   to   destroy  germs.     How  much   95  %   solution   will   be 
required  to  make  5  gallons  1  : 20  ? 

6.  1  : 1000  solution  means  how  many  grams  to  the  gallon  ? 

7.  A  normal  salt  solution  is  made  by  dissolving  9  grams 
of  salt  to  the  quart.     How  many  teaspoonfuls  to  the  quart? 
How  many  grains  to  the  quart  ? 

8.  What  is  the  ratio  of  a  pure  drug  ?     What  is  the  per- 
centage of  purity  of  a  pure  drug  ? 

9.  If  I  desire  to  make  a  lotion  of  1  : 1000  corrosive  subli- 
mate, how  much  of  the  substance  would  be  added  and  how 
much  water  used  ? 

10.  How  much  water  and  corrosive  sublimate  are  required 
for  a  gallon  of  the  following  strengths? 

a.  1:2000.  d.    1:20,000. 

b.  1:4000.  e.    1:100,000. 

c.  1:10,000.  /.    1:150,000. 

11.  A  saturated  solution  of  boric  acid  may  be  made  by  dis- 
solving 3  v  to  pint  (0  i)  of  water.    What  is  the  per  cent  of  the 
saturated  solution? 

12.  A  saturated  solution  of  KMn04  may  be  made  by  dis- 
solving §  i  to  0  i  ?     What  is  the  per  cent  ? 

13.  How  much  of  the  saturated  solution  should  be  added  to 
water  0  i  to  make  1  °/0  solution  ? 


296       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

Water  Analysis 

Every  nurse  should  be  able  to  interpret  a  biological  and 
chemical  analysis  of  water. 

Terms  used  in  Chemical  and  Bacteriological  Reports 

The  following  brief  explanation  of  the  terms  used  in  chemi- 
cal and  bacteriological  examinations  of  water  is  given  in  order 
that  the  reports  of  analyses  of  samples  may  be  clearly  under- 
stood. As  the  quantities  to  be  obtained  by  analyses  are  usu- 
ally very  small,  they  are  ordinarily  expressed  in  parts  per 
million  (p.  p.  m.),  and  always  by  weight. 

Turbidity  of  water  is  caused  by  fine  particles  such  as  clay, 
silt,  and  microscopic  organisms. 

Sediment  is  self-explanatory.  The  amount  and  nature  of 
the  sediment  are  usually  noted. 

Color  is  measured  by  comparing  the  sample  with  artificial 
standards  made  by  dissolving  certain  salts  in  distilled  water, 
or  sometimes  with  colored  glass  disks.  The  color  of  large 
lakes  is  usually  below  0.10. 

Odor.     This  requires  no  explanation. 

Residue  on  Evaporation,  or  Total  Solids,  indicates  the  total 
solid  matter,  both  organic  and  inorganic,  in  1,000,000  parts 
of  water.  The  determination  is  made  by  placing  about  100 
grams  of  water  in  a  platinum  dish  and  weighing  the  whole 
accurately.  The  water  is  then  evaporated  to  dryness  by  mod- 
erate heat  and  the  dish  again  weighed ;  the  difference  between 
this  and  the  weight  of  the  empty  dish  gives  the  total  solids  in 
the  water.  The  dish  is  then  heated  red  hot,  to  burn  out  the 
organic  matter,  when  the  weight  of  the  remaining  ash  gives 
the  inorganic  or  fixed  solids.  The  loss  on  ignition,  sometimes 
reported,  is  a  measure  of  the  organic  solids. 

Ammonia.  Ammonia  in  water  indicates  the  presence  of 
organic  matter  in  an  advanced  stage  of  decay,  and  although 


ARITHMETIC   FOR   NURSES  297 

the  amount  is  small,  it  affords  a  valuable  indication  of  what 
is  going  on  in  the  water.  It  is  determined  in  two  forms, 
called  "  free  "  and  "  albuminoid." 

Free  Ammonia  is  that  which  has  actually  been  set  free  in 
the  water  in  the  process  of  decay  of  organic  matter,  while 
Albuminoid  Ammonia  is  that  which  has  not  yet  been  set  free, 
but  which  is  liable  to  be  freed  under  the  action  of  the  oxygen 
in  the  water.  The  sum  of  the  two  gives  an  indication  of  the 
total  amount  of  organic  matter  in  the  water. 

Water  which  has  0.05  p.  p.  m.  of  free  ammonia  is  probably 
pure,  while  if  it  has  more  than  0.1  p.  p.  m.,  it  is  perhaps  dan- 
gerous. A  low  figure  for  albuminoid  ammonia  is  0.05  p.  p.  m., 
and  a  high  one  is  0.50. 

Chlorine  in  water  usually  represents  sodium  chloride,  or 
common  salt.  It  may  be  due  to  sewage  pollution  or  to  near- 
ness to  the  ocean.  It  is  always  found  in  natural  waters,  the 
normal  amount  decreasing  from  the  seacoast  inland.  If  the 
amount  exceeds  20  p.  p.  m.,  it  may  cause  corrosion  in  boilers 
and  plumbing  fixtures.  Properly  interpreted,  the  chlorine 
content  is  one  of  the  most  useful  indexes  of  the  extent  of 
sewage  pollution. 

Nitrogen  is  usually  determined  in  the  form  of  nitrates  and 
nitrites,  the  former  being  the  final  result  of  decomposition, 
while  the  latter  is  the  incomplete  result  of  the  same  action. 
If  an  analysis  shows  the  ammonia  to  be  low  and  the  nitrates 
high,  it  indicates  that  the  water  has  become  completely  puri- 
fied, while  the  reverse  indicates  that  the  decaying  process 
is  going  on  and  the  water  is  dangerous.  In  good  drinking 
water  the  nitrates  may  be  as  high  as  1  or  2  p.  p.  m.,  while 
the  nitrites,  if  present,  are  practically  always  a  sign  of  pol- 
lution. 

Oxygen  Consumed.  This  is  the  amount  of  oxygen  absorbed 
by  the  water  from  potassium  permanganate.  As  the  oxygen 
is  absorbed  by  the  organic  matter  present  in  the  water,  the 
amount  consumed  gives  a  measure  of  the  amount  of  impurities 


298       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

contained  in  it.  Less  than  1  p.  p.  m.  indicates  probable  pur- 
ity, while  as  high  as  4  or  5  p.  p.  m.  indicates  danger  in  drink- 
ing water. 

Hardness.  A  water  is  said  to  be  "  hard  "  when  it  contains 
in  solution  the  carbonates  and  sulphates  of  calcium  or  mag- 
nesium. When  a  hard  water  is  used  for  washing,  these  salts 
have  to  be  decomposed  by  soap  before  a  lather  can  be  formed. 
In  boilers,  a  hard  water  forms  scale.  Hardness  is  expressed 
by  the  number  of  parts  of  calcium  carbonate  in  1,000,000 
parts  of  water.  Rain  water  has  a  hardness  of  about  5,  and 
river  waters  of  from  50  to  100. 

Iron  may  be  troublesome  in  a  water  used  for  domestic  pur- 
poses if  it  is  present  in  quantities  greater  than  0.3  to  0.5 
p.  p.  m. 

Alkalinity  or  Temporary  Hardness  is  that  part  of  the  total 
hardness  which  is  due  to  carbonates  removable  by  boiling,  thus 
causing  the  formation  of  scale.  For  purposes  of  softening 
water  for  boiler  use,  it  is  necessary  to  know  both  the  total 
hardness  and  the  alkalinity. 

Bacteria.  While  it  is  obvious  that  the  quality  of  a  water  of 
turbid  appearance  and  unpleasant  odor  is  suspicious,  it  does 
not  follow  that  it  is  dangerous,  nor  is  a  water  which  is  entirely 
free  from  color  and  odor  necessarily  a  safe  drinking  water,  for 
epidemics  of  typhoid  have  been  caused  by  such.  The  bacteri- 
ological examination  of  water,  by  which  the  number  of  bacteria 
present  in  one  cubic  centimeter  (1  cc.)  is  determined,  is  there- 
fore an  important  part  of  an  analysis. 

As  a  general  statement,  it  may  be  said  that  fresh  water  con- 
taining less  than  100  bacteria  per  cc.  is  pure,  that  water  contain- 
ing 500  bacteria  per  cc.  should  be  viewed  with  suspicion,  and 
that  water  containing  1000  bacteria  per  cc.  is  undoubtedly  con- 
taminated. In  considering  these  figures  with  relation  to  a 
water  supply,  it  must  be  remembered  that  all  natural  surface 
waters  contain  some  bacteria  and  that,  except  where  there 
is  pollution,  the  greater  part  of  them  are  absolutely  harmless. 


ARITHMETIC    FOR   NURSES  299 

The  bacteria  are  so  small  that  they  may  be  seen  only  with 
the  aid  of  a  high-powered  microscope.  In  order  to  count  them 
a  culture  jelly  of  gelatine,  albumin,  and  extract  of  beef  is 
prepared  and  1  cc.  of  the  water  is  thoroughly  mixed  with 
10  cc.  of  the  culture  jelly,  a  small  measured  portion  of  this 
mixture  then  being  poured  in  a  thin  layer  on  a  sterilized  plate 
to  harden.  Each  bacterium  eats  and  multiplies  to  such  an 
extent  that  in  about  forty-eight  hours  a  visible  colony  is 
produced.  From  a  count  of  these  colonies  within  a  measured 
area  of  the  plate  the  number  of  bacteria  in  the  original  1  cc. 
of  water  is  determined. 

Different  species  of  bacteria  may  be  detected  by  the  use  of 
different  media  for  development,  or  they  may  be  found  by 
further  examination  with  the  microscope.  The  well-known 
colon  bacillus  (B.  coli),  which,  although  harmless  itself,  is  an 
indication  of  sewage  pollution,  is  detected  by  the  gas  which  it 
produces  in  a  closed  tube.  As  B.  coli  are  found  in  practically 
all  warm-blooded  animals  and  sometimes  in  fish  and  elsewhere, 
the  finding  of  a  few  in  large  samples  of  water,  or  their  occa- 
sional discovery  in  small  samples,  is  of  no  special  significance  ; 
but  if  they  are  found  in  a  larger  proportion  in  small  samples 
and  in  considerable  numbers  in  larger  ones,  sewage  pollution  is 
indicated. 

EXAMPLES 

1.  If  a  bacterium  multiplies  tenfold  every  half  hour  in  a 
person's   mouth,  how  many  will  be  produced  in  twenty-four 
hours  ? 

2.  A  sample  of  water  contains  0.24  parts  per  million  of  free 
ammonia.     How  many  parts  per  100,000  ? 

3.  A  sample  of  water  contains  1.1  parts  per  million  of  iron. 
How  many  parts  per  100,000  ? 

4.  A  sample  of  water  contains  10  parts  per  million  of  lime. 
How  many  parts  per  10,000  ? 


300       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


EXAMPLES  ON  ANALYSES   OF  WATER 

(Parts  in  100,000) 


KESIDUE  ON 
EVAPORATION 

AMMONIA 

NITROGEN 

AS 

Albuminoid 

Loss 

H 
Z: 

.    3 

1 

Total 

on 
Igni- 
tion 

Fixed 

Free 

Total 

In 
Solu- 
tion 

In 

Sus- 
pen- 
sion 

CHLORI 

Nitrate 

Nitrites 

ii 
II 

HARDN 

1 

a. 

4.00 

1.65 

2.35 

.0026 

.0190 

.0156 

.0034 

.72 

.0030 

.0001 

.31 

1.3 

.0160 

b. 

4.65 

2.00 

2.65 

.0028 

.0172 

.0148 

.0024 

.68 

.0030 

.0000 

.28 

1.3 

.0080 

c. 

3.85 

1.15 

2.70 

.0014 

.0148 

.0130 

.0018 

.68 

.0000 

.0000 

.31 

1.1 

.0080 

d. 

4.20 

1.50 

2.70 

.0052 

.0140 

.0128 

.0012 

.71 

.0000 

.0000 

.32 

1.1 

.0050 

c,. 

4.15 

1.35 

2.80 

.0018 

.0170 

.0152 

.0018 

.71 

.0000 

.0000 

.26 

1.0 

.0080 

f. 

5.00 

1.75 

3.25 

.0014 

.0162 

.0142 

.0020 

.73 

.0000 

.0000 

.36 

1.0 

.0120 

'/• 

4.35 

1.60 

2.75 

.0020 

.0178 

.0150 

.0028 

.70 

.0010 

.0001 

.24 

1.3 

.0080 

h. 

4.10 

1.15 

2.95 

.0018 

.0162 

.0136 

.0026 

.71 

.0010 

.0001 

.24 

1.3 

.0100 

1.  Give  the  number  of  parts  of  free  ammonia  in  10,000  in  a. 

2.  Give  the  number  of  parts  of  nitrates  in  10,000  in  b. 

3.  Give  the  number  of  parts  of  nitrites  in  10,000  in  d. 

REVIEW  EXAMPLES 

1.  Give   the   number   of   cubic   centimeters   of   water   you 
would  measure  out  to  get  the  following : 

a.  70  gm.  b.  11  kg.  c.  0.4  gm.  d.  61  mg. 

2.  How  much  would  the  following  amounts  of  water  weigh  ? 
a.  9  1.  b.  4.7  cc.  c.  1 1.  d.  48  cc. 

3.  If  the  dose  of  aromatic  spirits  of  ammonia  is  30  minims, 
what  is  the  dose  for  a  child  6  years  old  ? 

4.  Give  the  approximate  equivalents  in  household  measures 
of  the  following : 

a.  7  drams  c.  4  ounces  e.  12  fluid  ounces 

b.  36  grams  d.  90  minims  /.  3  fluid  drams 


ARITHMETIC   FOR   NURSES  301 

5.  Give  the  approximate  equivalents  in  household  measures 
of  the  following : 

a.  1500  cc.  c.  3  liters  e.  1  gramme 

6.  11  cc.  d.  0.003  grain  /.  0.008  gramme 

6.  How  many  grammes  in  3  ounces  of  1  %  solution  ? 

7.  How  many  drams  in  1  gallon  of  1  :  50  solution  ? 

8.  How  many  grammes  in  a  liter  of  10  %  solution  ? 

9.  How  many  grammes  in  5  liters  of  1  :  25  solution  ? 

10.  How  many  teaspoonfuls  of  pure  carbolic  acid  in  a  gallon 
of  1  %  solution  ? 

11.  How  many  drops  (minims)  of  carbolic  acid  in  a  quart 
of  1  : 1000  solution  ? 

12.  A  basin  of  rain  water  has  a  temperature  of  94°  F.     Give 
the  equivalent  on  the  Centigrade  scale. 

13.  A  cool  bath  registers  a  temperature  of  26°  C.     Give  the 
equivalent  on  the  Fahrenheit  scale. 

14.  A  dose  of  ipecac  is  20  to  30  grammes.     What  is  the  dose 
for  a  child  of  seven  years  ? 

15.  A  dose  of  1  :  500  solution  means  how  many  grammes  to 
a  quart? 

16.  Given  a  5%  solution  of  silver  nitrate,  how  would  you 
make  a  gallon  of  1 :  5000  solution  ? 

17.  How  would  you  make  a  gallon  of  3  %  solution  of  acetic 
acid  from  the  pure  acid  ? 

18.  How  would  you  make  two  quarts  of  5  %  solution  of  car- 
bolic acid  from  pure  acid  ?     (Consider  pure  acid  95  %.) 

19.  A  1 :  50  solution  is  used  for  disinfecting  wounds.     How 
would  you  make  a  gallon  of  this  fluid  from  standard  solution  ? 
(Consider  standard  strength  about  40  %.) 


302       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

20.  A  2  %   solution  of  boric  acid  is  used  for  eye  and  ear 
irrigations.     How  much  boric  acid  will  be  necessary  to  make  a 
quart  of  the  solution  ? 

21.  Give    the    approximate    equivalents     of    metric    and 
apothecaries'  measures  of  the  following : 

a.  31  cc.  d.   50  minims 

b.  yi¥  gram  e.    5  pints 

c.  1.6  gram  /.    101  cc. 

22.  If  the  pharmacy  nurse  buys  3  oz.  of  trional,  how  many 
powders  of  10  grains  each  can  she  make  ? 

23.  The  dose  of  the  tincture  of  opium  is  0.5  cc. ;  10  cc.  of 
the   tincture    contains    1    gm.    of   opium ;  12  %    of   opium   is 
morphine.     How  many  milligrams  of  morphine  in  one  dose  of 
the  tincture  ? 

24.  a.  Convert  the  following  to  milligrams :  5  dg.  and  0.27  gm. 
6.    Convert  the  following  to  grams  :  483  dg.  and  7  mg. 

25.  How  much  alcohol  (15  °/G  strength)  will  be  necessary  to 
make  a  quart  of  alcohol  containing  80  %  volume  of  absolute 
alcohol?     66%?     37%?     75%? 

26.  If  lactic  acid  is  composed  of  75  %  of  absolute  acid,  how 
much  absolute  acid  in  a  pound  of  the  official  preparation  ? 

27.  Diluted  alcohol  contains  41.5  %  absolute  alcohol.     How 
much  absolute  alcohol  in  a  gallon  of  dilute  alcohol  ? 

28.  The  dose  of  morphine  sulphate  is  0.008  gm.     What  is  the 
dose  for  a  baby  7  months  old  ? 

29.  The  dose  of  camphorated  tincture  of  opium  (paregoric) 
is  f  3  i.     What  is  the  dose  for  a  baby  6  months  old  ? 

30.  Hands  and  arms  are  often  disinfected  by  washing  in  a 
solution  of  permanganate  of  potash  (two  ounces  to  four  quarts 
of  water)  followed  by  immersion  in  a  solution  of  oxalic  acid 
(eight  ounces  to  four  quarts  of  water).     What  is  the  percentage 
of  each  ? 


ARITHMETIC   FOR   NURSES  303 

31.  Adhesive  iodoform  gauze  is  made  by  saturating  sterilized 
gauze  in  the  following  solution  : 

Iodoform  22  grams 
Resin          10  grams 
Glycerine  5  cc. 
Alcohol      26  cc. 

(Consider  specific  gravity  of  alcohol  and  glycerine  as  1.) 
What  per  cent  of  each  ?     Give  quantity  in  English  system. 

32.  How  much  of  each  ingredient  should  be  used  in  prepar- 
ing a  pound  of  the  following  mass  ? 

Zinc  oxide  5  parts 

Gelatine  5  parts 

Glycerine  12  parts 

Water  10  parts 

33.  What  per  cent  of  the  following   solution  is    atropine 

sulphate  ? 

Atropine  sulphate   1^  gr. 
Water  \  fluid  ounce 

34.  What  amount  of  carbolic  acid  crystals  is  used  to  make 
4  oz.  of  3  %  carbolized  petrolatum  ? 

35.  What  per  cent  of  the  following  solution  is  boric  acid  ? 

Boric  acid  18  gr. 
Water         1  oz. 

36.  How  much  bichloride  of  mercury  is  required  to  make 
1  qt.  of  a  1 : 25,000  solution  ? 

37.  How  much  potassium  permanganate  will  be  necessary 
to  make  a  pint  of  a  1 : 1000  solution  ? 


PART   VI  — PROBLEMS   ON   THE   FARM 


CHAPTER   XV 

EVERY  young  person  who  lives  on  the  farm  has  more  or  less 
to  do  with  the  bookkeeping  and  the  arithmetic  connected  with 
the  selling  of  the  eggs,  milk,  and  other  products.  Very  few 
of  the  men  on  the  farm  have  the  time  or  the  inclination  to  do 
this  work,  and  it  is  usually  performed  by  the  wife  or  daughter. 

EXAMPLES 

1.  I  sold  16  dozen  eggs  at  30  cents  a  dozen  and  took  my 
pay  in  butter  at  40  cents  a  pound.     How  many  pounds  did  I 
receive  ? 

2.  A  dealer  bought  16  cords  of  wood  at  $  4  a  cord  and  sold 
it  for  $  96.     Find  the  gain. 

3.  Three    men    bought  a    farm.      Henry   paid    $  1135.75, 
Philip   $2400.25,  and   Carl   as   much  as   Henry  and  Philip. 
Find  the  value  of  the  farm. 

4.  A  farmer  divided  his  farm  as  follows :  to  his  elder  son 
he  gave  257-f  acres,  to  his  younger  son  200fV  acres,  and  to  his 
wife  as  many  acres  as  to  his  two  sons.     How  many  acres  in 
the  farm  ? 

5.  One  farm  contains  287f  acres  and  another  244J  acres. 
Find  the  difference  between  them. 

6.  One  bin  contains  165^  bushels  of   grain  and  the  other 
bin  184^  bushels.     How  many  bushels  more  does  the  larger 
bin  contain  than  the  smaller  ? 

304 


PROBLEMS   ON    THE    FARM  305 

7.  From  a  farm  of  375J  acres,  84^  acres  were  sold.     How 
many  acres  remained  ? 

8.  A  farmer  owning  57f  acres  of  land  sold  281  acres  and 
afterwards  bought  141  acres.     How  many  acres  did  he  then 
own? 

9.  A   farm   contained    132    acres,    one-eighth   of  which   is 
woodland,   one-sixth  is  pasture,  and  the  remainder  is    culti- 
vated.    What  part  of  the  farm  is   cultivated  ?     How  many 
acres  are  cultivated  ? 

10.  From  four  trees,  14J  barrels  of  apples  were  gathered. 
One  man  bought  5^  bbl.,  another  31  bbl.     How  many  barrels 
remained  ? 

11.  I  owned  two-fifths  of  a  farm  and  sold  three-fourths  of 
my  share  for  $  1350.     Find  value  of  the  whole  farm. 

12.  I  bought  5  loads  of  potatoes  containing  331  bushels, 
27f  bushels,  40J  bushels,  35^  bushels,  and  29^  bushels.     I 
sold  12J  bushels  to  each  of  three  men,  and  25^-  bushels  to  each 
of  four  men.     How  many  bushels  were  left  ? 

13.  If  two-thirds  of  a  farm  costs  $  2480,  what  is  the  cost 
of  the  farm  ? 

14.  Mr.  Thomas  bought  168  sheep  at  $5.50  a  head.     He 
sold  three-sevenths  of  them  at  $  6  a  head,  and  the  remainder 
at  $  7  a  head.     Find  the  gain. 

15.  A  farm  is  divided  into  four  lots.     The  first  contains 
SOy7-^  acres,  the  second  4211  acres,  the  third  35^  acres,  the 
fourth  28|-  acres.     How  many  acres  in  the  farm  ? 

16.  A  farmer  sold  sheep  for  $  62.50,  cattle  for  $  102.60,  a 
horse  for  $  125.75,  and  a  plow  for  $  18.25.     How  much  did  he 
receive  ? 

17.  Farmer  Blake  raised  114  bushels   of  apples  and  73f 
bushels  of  pears.     How  many  more  bushels  of  apples  than 
pears  did  he  raise  ? 


306       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

18.  A  farmer  paid  $  78  for  a  cow,  $  165  for  a  horse.     How 
much  more  did  the  horse  cost  than  the  cow? 

19.  Mr.  Borden  has  450T7¥  acres  of  woodland  and  sells  304f 
acres.     How  much  has  he  left  ? 

20.  Mr.  Sherman  bought  ten  acres  of  land  at  $  65  an  acre 
and  sold  it  for  $  24.60  an  acre.     How  much  did  he  lose  ? 

21.  A's  farm  contains  265f-  acres,  B's  43^  acres.     What  is 
the  difference  in  the  size  of  their  farms  ? 

22.  Mr.  Grover  had  110  acres  of  land,  and  sold  7^%-  acres. 

'  ID 

How  many  acres  had  he  left  ? 

23.  Mr.  Dean  sold  one-third  of  his  farm  to  one  man,  one- 
fourth  to  another,  and  one-eighth  to  another.     What  part  had 
he  left  ? 

24.  I  paid  $  365.75  for  a  horse,  and  sold  him  for  four-fifths 
of  what  he  cost.     What  was  the  loss  ? 

25.  How  many  bushels  of  grain  can  be  put  into  16  bags,  if 
they  hold  2|  bushels  each  ? 

26.  A  farmer  carries  35  bushels  of  apples  to  market.     What 
is  half  this  load  worth  at  75  cents  a  bushel  ? 

27.  I  paid   $76.50  for  18  sheep.     What  was  the  average 
price  ? 

28.  Mr.  Platt  gave  435  acres  of  land  to  his  sons,  giving  each 
721  acres.     How  many  sons  had  he  ? 

29.  If  41  bushels  of  potatoes  were  bought  for  $  3.60,  how 
many  bushels  can  be  bought  for  $  10.80  at  the  same  price  per 
bushel  ? 

30.  Mr.  White  paid   $  16.25  for  2^  cords  of  wood.     How 
many  cords  could  he  buy  for  $  74.75  at  the  same  price  per 
cord? 

31.  A  father  divided  183  acres  of  land  equally  among  his 
sons,  giving  to  each  45  J  acres.     How  many  sons  had  he  ? 


PROBLEMS    ON    THE    FARM  307 

FARM  MEASURES 

(Review  Mensuration  and  Table  of  Measures.) 

1.  If  a  bushel  of  shelled  com  contains  1J  cubic  feet,  how 
many  bushels  in  a  bin  8'  x  4'  x  2'  6"? 

2.  A  bushel  of  ear  com  contains  21  cubic  feet.     How  many 
bushels  in  a  crib  10'  x  4'  3"  x  2'  4"  ? 

3.  A  ton  of  tame  hay  contains  512  cubic  feet.     How  many 
tons  in  a  space  14'  x  12'  x  13'  ? 

4.  A  ton  of  wild  hay  contains  343  cubic  feet.     How  many 
tons  in  a  space  28'  6"  x  18'  9"  x  13'  5"  ? 

5.  A   bushel   of    potatoes    contains   11   cubic   feet.     How 
many  bushels    in    a    bin    8'  6"  X  7'   5"  x  9'   3"   filled    with 
potatoes  ? 

6.  How  many  bushels  of  com  on  the  ear  in  a  pointed  heap 
12'  x  8' and  6' high? 

7.  How  many  bushels  of  corn  in  a  circular  crib  with  a 
diameter  12'  6"  and  a  height  8'? 

8.  How  many  gallons   of  water  in  a  rectangular  trough 
6'  3"  x  2f  6"  x  3'  4"  ?     (Consider  a  gallon  |  cubic  foot.) 

9.  How  many  acres  in  694  sq.  rods  ? 

10.  A   60-acre   piece  of  land,   half  a  mile  across,   is  6'  8" 
higher  on  one  side  than  the  other.     How  much  of  a  fall  (grade) 
to  the  rod  ? 

11.  How  many  bushels  of  corn  in  a  rectangular  crib  with 
sloping  sides  16'  long,  1'  high  and  4'  6"  wide  at  the  bottom  and 
6'  8"  wide  at  the  top  ? 

ENSILAGE  PROBLEMS 

1.  A  farmer  with  the  purpose  of  filling  his  silo  with  corn 
began  the  preparation  of  one  acre  of  land  for  planting :  8  loads 
of  stable  fertilizer  were  used  in  dressing  the  land.  What  is 
the  average  number  of  square  rods  a  load  will  fertilize  ? 


308       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

2.  The  field  was  plowed  in  a  day.     Mr.  A  receives,  when 
working  for  others,  20  cents  per  hour  for  his  horses  and  15 
cents   per  hour  for  his   own  work.     How  much  is  his  time 
worth  for  the  day  of  10  hours  ? 

3.  Mr.  A  paid  $  12  for  his  plow  and  two  extra  points.     The 
regular  price  without  extras  was  $  10.50.     Mr.  A  broke  a  plow 
point  on  a  rock.     How  much  was  the  loss  ? 

4.  It  took  three-fifths  as  long  to  harrow  the  field  (see  ex- 
ample 2)  as  to  plow  it.     If  the  work  was  begun  at  7  o'clock  in 
the  morning,  at  what  time  would  the  corn  piece  be  harrowed  ? 
(Noon  hour  from  12  M.  to  1  P.M.) 

5.  Mr.  A  bought  seed  com  at  $  1.25  per  bushel.     What 
did  the  seed  cost,  12  quarts  being  the  amount  used  ? 

6.  He  bought  4  one-hundred-pound  bags   of   fertilizer  at 
$  1.40  per  hundred.     How  much  did  the  fertilizer  cost  ? 

7.  Mr.   A  is  agent  for  Bradley  fertilizers  and  receives  a 
commission  of  10  %  on  what  he  sells  for  the  company.     How 
much  must  he  sell  to  receive  a  commission  equal  to  the  cost  of 
fertilizer  used  on  his  own  corn  piece,  and  also  the  expense  of 
hauling  from  the  railroad  station,  which  amounted  to  $  2.50  ? 

8.  Mr.  A  hires  a  man  to  plant  his  corn  with  a  horse  planter. 
He  pays  $  2  for  the  planting,  which  is  at  the  rate  of  30  ^  per 
hour.     How  long  did  it  take  ? 

9.  Mr.  A  cultivated  his  corn  three  times,  each  time  requir- 
ing about  8  hours.     Besides  this  he  and  his  hired  man  spent  3 
days  hoeing  the  corn  once.     Which  was  more  expensive,  the 
hoeing  or  the  cultivating  ?     How  much  ? 

10.  The  corn  was  planted  June  1st.     It  was  ready  for  cut- 
ting September  1st.     Some  of  the  stalks  had  grown  to  a  height 
of  6  ft.     What  was  the  average  weekly  growth  ? 

11.  Mr.  A's  silo  is  rectangular,  10  ft.  long,  10  ft.  wide,  and 
20  ft.  deep.     The  floor  is  cemented.     How  many  sq.  yd.  of 
cement  in  the  floor  ? 


PROBLEMS   ON    THE    FARM  309 

12.  If  the  lumber  is  1  inch  thick,  how  many  board  feet  in 
one  thickness  of  the  walls  ? 

13.  How  many  cubic  feet  of  ensilage  will  the  silo  hold  ? 
How  many  cubic  feet  below  the  level  of  the  bam  floor,  which 
is  5  ft.  higher  than  the  cemented  floor  of  the  silo  ? 

14.  How   many  bushels  of   the  cut  and  compressed    corn 
stalks  must  have  been  produced  on  the  acre  of  land  to  fill  the 
space  ? 

15.  On  September  1st  a  gang  of  men  helped  Mr.  A  fill  the 
silo.     Two  men  worked  in  the  field  cutting  down  the  stalks  at 
$  1.50  per  day  each.    Two  men  hauled  to  the  barn  with  teams  at 
$  3  per  day  each.     Two  men,  a  cutting  machine,  and  horses  for 
power  cost  $  7.     One  man  leveled  corn  in  the  silo  at  $  1.50 
per  day.     What  did  Mr.  A  pay  these  men  for  the  work  of  the 
day  ?     The  next  day  the  men  with  the  cutting  machine,  one 
man  with  a  team,  and  the  man  for  the  silo  worked  two  hours 
to  finish  the  work.     Add  this  expense  to  that  of  the  previous 
day. 

16.  A  week  later  the  ensilage  had  settled  8  feet  and  Mr.  A 
filled  the  space  with  surplus  corn.     He  and  a  helper  hoisted  it 
with  a  pulley  in  a  two-bushel  basket.     How  many  times  must 
he  fill  the  basket  ? 

17.  The  mass  was  left  to  the  fermenting  process  for  two 
months.     When  Mr.  A  opens  the  silo,  he  begins  feeding  regu- 
larly to  his  10  cows,  giving  each  one-half  bushel  twice  a  day. 
At  this  rate  when  will  the  silo  be  emptied?     When  should 
the  ensilage  be  even  with  the  barn  floor  ? 

18.  It  is  estimated  that  1  ton  of  ensilage  is  equal  in  value 
to  one-third  of  a  ton  of  hay.     If  ensilage  weighs  50  pounds 
per  bushel,  how  many  pounds  of  hay  equal  a  feed  of  ensilage  ? 

19.  How  many  tons  of  hay  is  the  ensilage  worth  ?     What 
is  the  value  at  $  15  per  ton  ? 


310       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

20.   Does  it  pay  the  farmer  to  raise  ensilage  ? 

NOTE.  —  Ensilage  could  not  be  used  as  a  substitute  for  hay,  but  is  ex- 
cellent as  a  milk  producer  when  fed  in  moderate  quantities.  Cows  like 
it  better  than  hay. 

DAIRY  PRODUCE 

Milk  is  graded  according  to  the  amount  of  cream  (fat)  in  it. 
In  addition  to  cream,  it  contains  casein  (cheese),  milk  sugar, 
and  about  84  %  water.  Milk  is  usually  sold  by  the  farmer  by 
weight  and  the  per  cent  cream. 

To  illustrate  :  A  sample  of  milk  from  a  large  can  weighing 
50  Ib.  contains  4  %  cream.  The  large  can  contains  2  Ib.  of 
butter  fat. 

EXAMPLES 

1.  A  sample  of  milk  from  a  cooler  containing  48-J-  Ib.  tested 
3J  %  butter  fat.     How  much  butter  fat  in  the  cooler  ? 

2.  A  cow  gives  3J  gallons  of  milk  per  day.     If  a  gallon 
weighs  8f  Ib.,  what  is  the  weight  of  milk  per  day  ?  per  week  ? 
per  month  ? 

3.  If  the  milk  in  example  2  contains  4.7  per  cent  of  cream, 
how  much  butter  fat  does  it  yield  per  week  ?  per  month  ? 

4.  If  butter  fat  is  worth  26  cents  a  pound,  how  much  is  ob- 
tained per  week  from  the  butter  fat  in  example  3  ?     How  much 
per  month  ? 

5.  Another  cow  gives  3-|  gallons  of  milk  a  day  that  tests 
4.6  %  butter  fat.     Is  it  more  profitable  to  keep  this  cow  or  the 
one  in  examples  2  and  3,  and  by  how  much  ? 

6.  Skim  milk  from  the  butter  fat  is  usually  sold  to  feed  the 
pigs  at  5J  cents  a  gallon.    Is  it  cheaper  to  sell  milk  at  5^  cents 
a  quart  or  to  make  butter  and  sell  it  at  26  cents  a  pound  and 
give  the  skim  milk  to  the  pigs  ? 


PROBLEMS   ON   THE    FARM  311 

PROBLEMS   ON   EQUIPPING   A   COOPERATIVE   CHEESE   FACTORY 

Seventy-three  farmers  came  together,  and  after  the  election 
of  officers  it  was  decided  that  a  stock  company  of  seventy-three 
shares  should  be  formed,  and  each  member  bought  a  share  at 
the  rate  of  $  75.  Part  of  the  money  was  used  to  erect  a  cheese 
factory,  and  the  rest  was  deposited  in  a  bank  and  drawn  out 
as  it  was  needed  to  run  the  business  until  the  sale  of  the 
products  should  be  sufficient  to  supply  money  for  carrying  on 
the  business  and  paying  a  small  per  cent  on  the  money  invested 
by  each  man.  The  following  are  the  items  of  expense  : 

Half  acre  of  land  at  $0.03  a  square  foot. 

The  building  cost  $  2000  for  material  and  work. 

Three  large  vats,  $  50  each  ;  4  %  discount. 

A  Babcock  tester  $30  ;  2|  %  discount. 

A  small  engine,  belts,  etc.,  $53.85. 

Whey  trough  and  leads,  $  54  ;  4  °Jo  discount. 

Cheese  press,  $  28  ;  3  %  discount. 

Rennet,  salt,  coloring,  wood,  cheesecloth,  boiler,  and  piping,  $15. 

Boxes,  acid  for  test,  etc.,  $  57  ;  3  %  commission. 

Scales,  weights,  and  weighing  can,  $27.85. 

A  year's  salary  to  the  cheese  maker,  $  520. 

The  money  left  after  these  expenses  was  put  at  3  %  interest. 

PROBLEMS 

1.  How  much  money  was  put  into  the  business  ? 

2.  How  much  did  the  cheese  maker  average  a  week  ? 

3.  What  was  the  cost  of  the  land  ? 

4.  The  man  who  sold  the  boiler   and  piping  and  also  the 
engine  and   belt   to   the   company  received  6  %  commission. 
What  did  he  receive  for  his  sales  ? 

5.  The  man  who  bought  the  whey  trough,  the  leads,  and 
the  large  vats  received  the  discount  as  his  commission.     How 
much  did  he  receive  ? 

6.  How  much  did  the  company  that  sold  the  whey  trough, 
leads,  and  vats  receive  ? 


312       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

7.  How  much  did  the  buying  company  pay  out  for  the  whey 
trough,  leads,  and  vats  ? 

8.  An  agent  sold  the  tester  ;  his  commission  was  5  %.    How 
much  did  he  receive  ? 

9.  How  much  did  the  tester  cost  the  company  ? 

10.  The  man  who  bought  the  press  and  material  received 
3  °/o  commission.     How  much  did  the  press  and  materials  cost 
the  company? 

11.  How  much  did  it  cost  to  buy  the  land,  build  the  fac- 
tory, and  equip  the  plant  ? 

12.  How  much  was  left  at  interest  ? 

13.  How  much  would  the  interest  be  for  3  years  6  months 
and  16  days  ? 

14.  What  is  the  interest  for  one  year  ? 

15.  What  per  cent  of  the  whole  investment  is  this  interest  ? 

16.  What  per  cent  of  the  whole  was  left  at  interest  ? 

PROBLEMS  ON  POULTRY 

One  hen  has  to  have  five  square  feet  of  room  in  the  house. 

It  costs  about  ten  cents  a  month  to  feed  one  hen. 

One  dozen  eggs  sell  on  the  average  for  30  cents. 

One  hen  lays  about  100  eggs  per  year. 

Broilers  are  sold  at  25  cents  a  pound. 

Hens  are  sold  for  15  cents  a  pound. 

An  incubator  costing  $  20  holds  150  eggs. 

Setting  eggs  cost  $  1.00  a  dozen. 

Brooders  cost  $7.50. 

A  small  chicken  coop  costs  $  8.00. 

One  hen  costs  60  cents. 

Little  chickens  1  week  old  cost  10  cents. 

Chicken  wire,  6  ft.  wide,  costs  4J-  cents  per  foot. 


PROBLEMS   ON   THE    FARM  313 

PROBLEMS 

1.  How  large  would  the  floor  of  my  poultry  house  have  to 
be  for  30  chickens  ?  for  50  ?  80  ?  200  ? 

2.  If  I  have  a  poultry  house  the  floor  of  which  is  30  ft.  by 
50  ft.,  how  many  chickens  can  I  put  in  it? 

3.  How  much  will  it  cost  to  keep  the  chickens  one  month  ? 
one  year  ? 

4.  If  I  have  one  hen,  how  much  does  it  cost  me  to  feed  her 
one  year?     Suppose  she  lays  90  eggs,  how  much  will  I  receive 
for  them  ?     Does  it  pay  me  to  keep  the  hen  ? 

5.  Suppose  I  sold  25  broilers,  12  weighing  3  lb.,  5  weigh- 
ing 5  lb.,  and  the  rest  an  average  of  4  lb.     How  much  would  I 
receive  for  them  ?     If  I  had  kept  them  14  weeks,  how  much 
would  they  have  cost  me  ?     Would  I  gain  or  lose  in  keeping 
them  ?     How  much  ? 

6.  If  I  bought  an  incubator  for  $  20,  a  brooder  for  $  7.50, 
a  chicken  coop  for  $  8,  and  150  eggs  to  put  into  the  incubator, 
how  much  did  I  pay  in  all  ? 

7.  If  from  the  150  eggs  only  139  were  hatched  and  lived, 
how  much  would  I  receive  for  the  little  chickens  when  I  sold 
them? 

8.  Suppose  I  had  a  chicken  yard  100  by  250  ft.     How  many 
feet  of  wire  would  I  need  to  fence  it  in  ?     How  much  would 
it  cost  me  to  put  wire  around  it  ? 

9.  How  many  eggs  would  I  receive  from  60  hens  in  one 
year  ?     If  I  sold  all  from  40  hens,  how  much  would  I  receive 
for  them  ? 

10.  If  I  bought  50  little  chickens,  kept  them  16  weeks,  and 
then  sold  them,  each  weighing  on  the  average  3  lb.,  how  much 
profit  did  I  make  on  them  ? 


314       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

POULTRY  RAISING 

1.  A  man  wishes  to  build  and  stock  a  henhouse  for  $  125. 
If  he  has  $  75,  how  much  will  he  have  to  borrow  ?     How  much 
interest  will  -he  have  to  pay  for  1  year  at  5  %  ? 

2.  If  he  pays  $  20  for  labor,  three  times  as  much  for  mate- 
rial, one-fourth  as  much  for  apparatus  as  for  material,  how 
much  will  he  have  left  ?     How  many  hens  could  he  buy  with 
the  remainder  if  each  hen  cost  50  cents  ? 

3.  If  it  cost  $  1  per  year  to  keep  one  hen,  how  much  would 
it  cost  to  keep  all  of  his  hens  for  1  year  ?  for  5  years  ? 

4.  If  each  hen  lays  100  eggs  a  year,  how  many  eggs  would 
they  yield  in  one  year  ?  how  many  dozen  ? 

5.  If  he  sold  400  dozen  at  25  cents  per  dozen,  how  much 
would  he  receive  for  them  ? 

6.  If  he  sold  the  remaining  dozen  "  for  setting  "  at  50  cents 
a  dozen,  how  much  would  he  receive  for  these  ?     How  much 
did  he  receive  for  all  his  eggs  ? 

7.  If  it  cost  him  the  above  amount  to  keep  the  hens  for  a 
year,  how  much  did  he  gain  from  selling  his  eggs  ? 

8.  If,  from  100  dozen  eggs  sold  for  "  setting,"  9  chickens 
were   hatched   from   each    dozen,   how   many   chickens   were 
hatched  in  all  ? 

9.  If  it  cost  him  27  cents  to  raise  one  broiler,'  how  much 
would  it  cost  to  raise  all  the  chickens  for  broilers  ? 

10.  If  for   each   pair  of  broilers   he   received    $  1.50,  how 
much  would  his  entire  stock  net  him  ? 

11.  After  considering  the  cost  of  raising  the  broilers  and 
the  price  received  for  them,  what  was  his  profit  ? 

12.  After    he    had    paid    his    interest,   what   was   his   net 
profit  ? 


PROBLEMS   ON    THE    FARM  315 

REVIEW  EXAMPLES 

1.  A  crib  of  corn  is  12'  wide,  34'  long,  and  has  an  average 
depth  of  11'  of  corn  in  it.     How  many  bushels  ? 

2.  How  many  bushels  of  oats  in  a  bin  12'  wide,  12'  long, 
18'  deep  ? 

3.  A  freight  car  is  8'  x  32'  x  11'.     If  it  is  filled  3f '  deep 
with  apples  for  the  cider  mill,  how  many  bushels  in  the  car  ? 

4.  At  26  cents  a  barrel,  what  is  the  car  of  apples  worth  ? 
(2-i  bu.  =  1  bbl.) 

5.  A  field  of  hay  is  88  rods  long  and  64  rods  wide.     How 
much  is  it  worth  at  $  98  an  acre  ? 

6.  A  cow  gives  3f  gallons  of  milk  a  day.     The  milk  tests 
4.2  %  butter  fat.     At  27  cents  a  pound  for  butter,  and  5  cents 
a  quart  for  skim  milk,  how  much  is  obtained  a  week  from  this 
cow? 

7.  A  flock  of  200  hens  averaged  135  eggs  a  year,  and  at 
the  end  of  four  years  were  sold  for  10|  cents  a  pound,  the 
average  weight  being  6J-  lb.     If  the  cost  of  feed  for  a  year  is 
$  27.05  for  the  whole  flock,  what  is  the  average  gain  per  hen  ? 

8.  A  man  receives  S  35  a  month.     How  much  per  hour,  if 
the  month  contains  26  working  days  of  10  hours  a  day  ? 

9.  What  is  the  cost  of  963J  bushels  of  oats  at  47  cents  per 
bushel? 

10.   If  I  buy  125  bushels  of  corn  at  41|  cents  per  bushel 
and  sell  it  at  52^  cents  a  bushel,  how  much  do  I  gain  ? 


APPENDIX 

METRIC  SYSTEM 

THE  metric  system  is  used  in  nearly  all  the  countries  of 
Continental  Europe  and  among  scientific  men  as  the  standard 
system  of  weights  and  measures.  It  is  based  on  the  meter  as 
the  unit  of  length.  The  meter  is  supposed  to  be  one  ten- 
millionth  part  of  the  length  of  the  meridian  passing  from  the 
equator  to  the  poles.  It  is  equal  to  about  39.37  inches.  The 
unit  of  weight  is  the  gram1  which  is  equal  to  about  one 
thirtieth  of  an  ounce.  The  unit  of  volume  is  the  liter,  which 
is  a  little  larger  than  a  quart. 

Measures  of  Length 

10  millimeters  (mm.)     .     .     .     .     =  I  centimeter cm. 

10  centimeters =1  decimeter dm: 

10  decimeters =1  meter m. 

10  meters =1  dekameter Dm. 

10  dekameters =1  hektometer Hm. 

10  hektometers =1  kilometer Km. 

Measures  of  Surface  (not  Land) 

100  square  millimeters  (mm.)  .  .  =1  square  centimeter  .  .  sq.  cm. 
100  square  centimeters  ..-.=!  square  decimeter  .  .  sq.  dm. 
100  square  decimeters  .  .  .  .  =  1  square  meter sq.  m. 

.    Measures  of  Volume 

1000  cubic  millimeters  (mm.)  .  .  =  1  cu.  centimeter  .  .  .  cu.  cm. 
1000  cubic  centimeters  .  .  .  .  =  1  cubic  decimeter  .  .  .  cu.  dm. 
1000  cubic  decimeters  .  .  .  .  =  1  cubic  meter cu.  m. 

1  The  gram  is  the  weight  of  one  cubic  centimeter  of  pure  distilled  water  at 
a  temperature  of  39.2°  F. ;  the  kilogram  is  the  weight  of  1  liter  of  water ;  the 
metric  ton  is  the  weight  of  1  cubic  meter  of  water. 

317 


318       VOCATIONAL  MATHEMATICS  FOR  GIRLS 


Measures  of  Capacity 

10  milliliters  (ml.) =1  centiliter 

10  centiliters .     =  1  deciliter 

10  deciliters 


=  1  liter 


10  liters =1  dekaliter 


cl. 

dl. 

1. 

Dl. 


10  dekaliters 


=  1  hektoliter  .  HI. 


10  hektoliters =1  kiloliter 


Kl. 


Measures  of  Weight 


10  milligrams  (mg.) 

10  centigrams    .  . 

10  decigrams     .  . 

10  grams       .     .  . 

10  dekagrams    .  . 
10  hektograms  . 
1000  kilograms 


centigram eg. 

decigram dg. 

gram g. 

dekagram  ......  Dg. 

hektogram ......  Hg. 

kilogram Kg. 


=  1  ton 


1  meter 
1  centimeter 
1  millimeter 
1  kilometer 
1  foot 
1  inch 


METRIC  EQUIVALENT  MEASURES 
Measures  of  Length 

=  39.37  in.  =  3.28083  ft.=  1.0936  yd. 

=      .3937  inch 

=      .03937  inch,  or  -fa  inch  nearly 

=      .62137  mile 

=      .3048  meter 

=    2.54  centimeters  =  25.4  millimeters 


Measures  of  Surface 

1  square  meter          =  10.764  sq.  ft.  =  1.196  sq.  yd. 
1  square  centimeter  =      .155  sq.  in. 

.00155  sq.  in. 

.836  square  meter 

.0929  square  meter 
6.452  square  centimeters =645. 2  square  millimeters 


1  square  millimeter  = 
1  square  yard 
1  square  foot  = 

1  square  inch  = 


Measures  of  Volume  and  Capacity 

1  cubic  meter  =  35.314  cu.  ft.  =  1.308  cu.  yd.  =  264.2  gal. 

1  cubic  decimeter     =  61.023  cu.  in.  =  .0353  cu.  ft. 
1  cubic  centimeter    =      .061  cu.  in. 

1  The  liter  is  equal  to  the  volume  occupied  by  1  cubic  decimeter. 


METRIC   SYSTEM  319 

1  liter  =  1  cubic  decimeter  =  61.023  cu.  in.  =  .0353  cu.  ft.  = 

1.0567  quarts   (U.  S.)=.2642  gallon  (U.  S.)  = 
2.202  Ib.  of  water  at  62°  F. 

cubic  yard  =      .7645  cubic  meter 

cubic  foot  =      .02832  cubic  meter  =  28.317  cubic  decimeters  = 

28.317  liters 

cubic  inch  =  16.387  cubic  centimeters 

gallon  (British)      =    4.543  liters 
gallon  (U.  S.)        =    3.785  liters 

Measures  of  Weight 

1  gram  =  15.432  grains 

1  kilogram  =    2.2045  pounds 

1  metric  ton  =      .9842  ton  of  2240  Ib.  =  19.68  cwt.  =  2204.6  Ib. 

1  grain  =      .0648  gram 

1  ounce  avoirdupois  =  28.35  grams 

1  pound  =      .4536  kilogram 

1  ton  of  2240  Ib.       =    1.016  metric  tons  =  1016  kilograms 

Miscellaneous 

1  kilogram  per  meter  =  .6720  pound  per  foot 

1  gram  per  square  millimeter  =  1.422  pounds  per  square  inch 

1  kilogram  per  square  meter  =  .2084  pound  per  square  foot 

1  kilogram  per  cubic  meter  =  .0624  pound  per  cubic  foot 

1  degree  centigrade  —  1.8  degrees  Fahrenheit 

1  pound  per  foot  =  1.488  kilograms  per  meter 

1  pound  per  square  foot  =  4.882  kilograms  per  square  meter 

1  pound  per  cubic  foot  =  16.02  kilograms  per  cubic  meter 

1  degree  Fahrenheit  =  .5556  degree  centigrade 

1  Calorie  (French  Thermal  Unit)  =  3.968  B.  T.  U.  (British  Thermal  Unit) 

1  horse  power  =  33,000  foot  pounds  per  minute  =  746  watts 

1  watt  (Unit  of  Electrical  Power)  =  .00134  horse  power  =  44.24  foot 

pounds  per  minute 
1  kilowatt  =  1000  watts  =  1.34  horse  power =44,240  foot  pounds  per  minute 

TABLE  OF  METRIC  CONVERSION 

To  change  meters  to  feet multiply  by  3.28083 

feet  to  meters multiply  by  .3048 

square  feet  to  square  meters       .     .     .  multiply  by  .0929 

square  meters  to  square  feet      .     .     .  multiply  by  10.764 


320       VOCATIONAL  MATHEMATICS  FOR   GIRLS 

To  change  square  centimeters  to  square  inches    .  multiply  by        .155 

square  inches  to  square  centimeters    .  multiply  by      6.452 

inches  to  centimeters multiply  by      2.54 

centimeters  to  inches multiply  by        .3937 

grams  to  grains multiply  by  15.43 

grains  to  grams multiply  by        .0648 

grams  to  ounces multiply  by        .0353 

ounces  to  grams multiply  by  28.35 

pounds  to  kilograms multiply  by        .4536 

kilograms  to  pounds multiply  by      2.2045 

liters  to  quarts multiply  by      1.0567 

liters  to  gallons multiply  by        .2642 

gallons  to  liters multiply  by      3.78543 

liters  to  cubic  inches multiply  by  61.023 

cubic  inches  to  cubic  centimeters    .     .  multiply  by  16.387 

cubic  centimeters  to  cubic  inches    .     .  multiply  by        .061 

cubic  feet  to  cubic  decimeters  or  liters  multiply  by  28.317 

kilowatts  to  horse  power multiply  by       1.34 

calories  to  British  Thermal  Units   .     .  multiply  by      3.968 

EXAMPLES 

1.  Change  8  m.  to  centimeters  ;  to  kilometers. 

2.  Reduce  4  Km.,  6  m.,  and  2  m.  to  centimeters. 

3.  How  many  square  meters  of  carpet  will  cover  a  floor 
which  is  25.5  feet  long  and  24  feet  wide  ? 

4.  (a)  Change  6J5  centimeters  into  inches. 

(6)  Change  48.3  square  centimeters  into  square  inches. 

5.  A  cellar  18  m.  x  37  m.  x  2  m.  is  to  be  excavated ;  what 
will  it  cost  at  13  cents  per  cubic  meter  to  do  the  work  ? 

6.  How   many  liters  of   capacity  has   a  tank   containing 
5.2  cu.  m.  ? 

7.  What  is  the  weight  in  grams  of  31  cc.  of  water  ? 

8.  Give  the  approximate  value  of  36  millimeters  in  inches. 

9.  Change  84.9  square  meters  into  square  feet. 
10.    Change  23.6  liters  to  cubic  inches. 


METRIC   SYSTEM  321 

11.  Change    7.3   m.    to   millimeters ;    to    centimeters ;    to 
kilometers. 

12.  Reduce  9.8  m.  to  kilometers ;  to  centimeters ;  to  milli- 
meters. 

13.  What  is  the  difference  in  millimeters  between  2.7  m. 
and  48.1  mm.  ? 

14.  What  part  of  a  kilometer  is  1.8  mm.  ? 

15.  What  part  of  a  meter  is  1.3  cm.  ? 

16.  How  many  square  centimeters  are  there  in  26  square 
kilometers  ? 

17.  How   many   square  meters   in  4   rectangular   gardens, 
3.4  Dm.  long  and  85.7  dm.  wide  ? 

18.  How  many  cubic  meters  in  a  wall  43  m.  long,  8.4  dm. 
high,  and  69  cm.  wide  ? 

19.  Reduce  869.7  eg.  to  milligrams  ;  to  kilograms  ;  to  grams. 

20.  What   is  the  weight   in   grams  of  48.7   cc.  of   water  ? 
What  is  the  weight  in  kilograms  of  43.9  1.  of  water? 

21.  Mercury  weighs  13.6  times  as  much  as  water ;  what  is 
the  weight  of  87.5  cc.  of  mercury  ?     Of  5  1.  of  mercury  ? 

22.  A  tank  is  7.9  m.  by  4.3  m.  by  3.1  m.     How  many  grams 
of  water  will  it  hold  ? 

23.  What  is  the  weight  of  874  cc.  of  copper,  the  density  of 
which  is  89  g.  per  cubic  centimeter  ? 

24.  What  is  the  capacity  of  a  bottle  that  holds  5  kg.  of 
alcohol,  the  density  of  which  is  0.8  g.  per  cubic  centimeter  ? 

25.  What  is  the  weight  in  grams  of  56.8  cc.  of  alcohol? 
What  is  the  weight  in  kilograms  of  7  1.  of  alcohol  ? 

26.  What  part  of  a  liter  is  1.7  cc.  ? 


GRAPHS 

A  SHEET  of  paper,  ruled  with  horizontal  and  vertical  lines 
that  are  equally  distant  from  each  other,  is  called  a  sheet  of 
cross-section,  or  coordinate,  paper.  Every  tenth  line  is  very 
distinct  so  that  it  is  easy  for  one  to  measure  off  the  horizontal 
and  vertical  distances  without  the  aid  of  a  ruler.  Ruled  or 


0 

UJ§ 
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-  :• 

-t 

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:',< 

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r- 

.t 

soislsils|=2 

"°ss  —  =  <  =  ?  <s 

£ 

30 

on 

90 

on 

op 

PI 

9ft 

J 

\ 

97  - 

> 

V 

•27 

V 

L      . 

96  - 

1   J 

•26 

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\\ 

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k 

94  - 

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O  4 

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OQ    . 

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1  ft  - 

1  8 

GRAPH  SHOWING  THE  VARIATION  IN  PRICE  OF  COTTON  YARN  FOR  A 
SERIES  OF  YEARS 

coordinate  paper  is  used  to  record  the  rise  and  fall  of  the 
price  of  any  commodity,  or  the  rise  and  fall  of  the  barometer 
or  thermometer. 

Trade  papers  and  reports  frequently  make  use  of  coordinate 
paper  to  show  the  results  of  the  changes  in  the  price  of  com- 
modities. In  this  way  one  can  see  at  a  glance  the  changes 

322 


GRAPHS  323 

and  condition  of  a  certain  commodity,  and  can  compare  these 
with  the  results  of  years  or  months  ago.  He  also  can  see 
from  the  slope  of  the  curve  the  rate  of  rise  or  fall  in  price. 

If  similar  commodities  are  plotted  on  the  same  sheet,  the 
effect  of  one  on  the  other  can  be  noted.  Often  experts  are 
able  to  prophesy  with  some  certainty  the  price  of  a  commodity 
for  a  month  in  advance.  The  two  quantities  which  must  be 
employed  in  this  comparison  are  time  and  value,  or  terms 
corresponding  to  them. 

The  lower  left-hand  corner  of  the  squared  paper  is  generally 
used  as  an  initial  point,  or  origin,  and  is  marked  0,  although 
any  other  corner  may  be  used.  The  horizontal  line  from  this 
corner,  taken  as  a  line  of  reference  or  axis,  is  called  the  ab- 
scissa. The  vertical  line  from  this  corner  is  the  other  axis, 
and  is  called  the  ordinate. 

Equal  distances  on  the  abscissa  (horizontal  line)  represent 
definite  units  of  time  (hours,  days,  months,  years,  etc.),  while 
equal  distances  along  the  ordinate  (vertical  line)  represent 
certain  units  of  value  (cost,  degrees  of  heat,  etc.). 

By  plotting,  or  placing  points  which  correspond  to  a  certain 
value  on  each  axis  and  connecting  these  points,  a  line  is  ob- 
tained that  shows  at  every  point  the  relationship  of  the  line 
to  the  axis. 

EXAMPLES 

1.  Show  the   rise   and    fall  of  temperature  in  a  day  from 
8  A.M.  to  8  P.M.,  taking  readings  every  hour. 

2.  Show  the  rise  and  fall  of  temperature  at  noon  every  day 
for  a  week. 

3.  Obtain  stock  quotation  sheets  and  plot  the  rise  and  fall 
of  cotton  for  a  week. 

4.  Show  the  rise  and  fall  of  the  price  of  potatoes  for  two 
months. 

5.  Show  a  curve  giving  the  amount  of  coal  used  each  day 
for  a  week. 


FORMULAS 

MOST  technical  books  and  magazines  contain  many  formulas. 
The  reason  for  this  is  evident  when  we  remember  that  rules 
are  often  long  and  their  true  meaning  not  comprehended  until 
they  have  been  reread  several  times.  The  attempt  to  abbre- 
viate the  length  and  emphasize  the  meaning  results  in  the 
formula,  in  which  whole  clauses  of  the  written  rule  are  ex- 
pressed by  one  letter,  that  letter  being  understood  to  have 
throughout  the  discussion  the  same  meaning  with  which  it 
started. 

To  illustrate  :  One  of  the  fundamental  laws  of  electricity  is  that  the 
quantity  of  electricity  flowing  through  a  circuit  (flow  of  electricity)  is 
equal  to  the  quotient  (expressed  in  amperes)  obtained  by  dividing  the 
electric  motive  force  (pressure,  or  expressed  in  volts,  voltage)  of  the 
current  by  the  resistance  (expressed  in  ohms). 

One  unfamiliar  with  electricity  is  obliged  to  read  this  rule  over  several 
times  before  the  relations  between  the  different  parts  are  clear.  To  show 
how  the  rule  may  be  abbreviated, 

Let  7  =  quantity  of  electricity  through  a  wire  (amperes) 
E  —  pressure  of  the  current  (volts) 
E  =  resistance  of  the  current  (ohms) 

Then  1=  E+  £  =  - 

It  is  customary  to  allow  the  first  letter  of  the  quantity  to  represent  it  in 
the  formula,  but  in  this  case  I  is  used  because  the  letter  C  is  used  in  an- 
other formula  with  which  this  might  be  confused. 

Translating  Rules  into  Formulas 

The  area  of  a  trapezoid  is  equal  to  the  sum  of  the  two  parallel 
sides  multiplied  by  one  half  the  perpendicular  distance  between 
them. 

324 


FORMULAS  325 

We  may  abbreviate  this  rule  by  letting 

A  =  area  of  trapezoid 

L  =  length  of  longest  parallel  side 

M=  length  of  shortest  parallel  side 

JV  =  length  of  perpendicular  distance  between  them 

Then  A  =  (L  +  M  )  x  ^,  or 

2 


The  area  of  a  circle  is  equal  to  the  square  of  the  radius 
multiplied  by  3.1416.  When  a  number  is  used  in  the  formula 
it  is  called  a  constant,  and  is  sometimes  represented  by  a  letter. 
In  this  case  3.1416  is  represented  by  the  Greek  letter  TT  (pi)  . 

Let  A  =  area  of  circle 

E  =  radius  of  circle 

Then  A  =  IT  x  jR2,  or  (the  multiplication  sign  is  usually  left  out  between 
letters) 


Thus  we  see  that  a  formula  is  a  short  and  simple  way  of 
stating  a  rule.  Any  formula  may  be  written  or  expressed  in 
words  and  is  then  called  a  rule.  The  knowledge  of  formulas 
and  of  their  use  is  necessary  for  nearly  every  one  engaged  in 
the  higher  forms  of  mechanical  or  technical  work. 

*  When  two  or  more  quantities  are  to  be  multiplied  or  divided  or  other- 
wise operated  upon  by  the  same  quantity,  they  are  often  grouped  together 
by  means  of  parentheses  (  )  or  braces  {  },  or  brackets  [  ].  Any  number 
or  letter  placed  before  or  after  one  of  these  parentheses,  with  no  other 
sign  between,  is  to  multiply  all  that  is  grouped  within  the  parentheses. 

In  the  trapezoid  case  above,  —  is  to  multiply  the  sum  of  L  and  Jf,  hence 

the  parentheses.     To  prevent  confusion,  different  signs  of  aggregation 
may  be  used  for  different  combinations  in  the  same  problem. 
For  instance, 

V=  \TrH\*(r*  +  r'2)  +  ^2]  which  equals 
o        L  2  2  J 

V  = 


326       VOCATIONAL  MATHEMATICS  FOR  GIRLS 

EXAMPLES 

Abbreviate  the  following  rules  into  formulas : 

1.  One  electrical  horse  power  is  equal  to  746  watts. 

2.  One  kilowatt  is  equal  to  1000  watts. 

3.  The  number  of   watts   consumed  in.  a  given   electrical, 
circuit,  such  as  a  lamp,  is  obtained  by  multiplying  the  volts  by 
the  amperes. 

4.  The  number  of  volts  equals  the  watts  divided  by  the 
amperes. 

5.  Number  of  amperes  equals  the  watts  divided  by  the 
volts. 

6.  The  horse  power  of  an  electric  machine  is  found  by  mul- 
tiplying the  number  of  volts  by  the  number  of  amperes  and 
dividing  the  product  by  746. 

7.  The  speed  at  which  a  body  travels  is  equal  to  the  ratio 
between  the  distance  traveled  and  the  time  which  is  required. 

8.  To  find  the  pressure   in  pounds  per  square  inch   of   a 
column  of  water,  multiply  the  height  of  the  column  in  feet  by 
0.434. 

9.  The  amount  of  gain  in  a  business  transaction  is  equal  to 
the  cost  multiplied  by  the  rate  of  gain. 

10.  The  selling  price  of  a  commodity  is  equal  to  the  cost 
multiplied  by  the  quantity  100  %  plus  the  rate  of  gain. 

11.  The  selling  price  of  a  commodity  is  equal  to  the  cost 
multiplied  by  the  quantity  100  %  minus  the  rate  of  loss. 

12.  The  interest  on  a  sum  of  money  is  equal  to  the  product 
of  the  principal,  time  (expressed  as  years),  and  the  rate  (ex- 
pressed as  hundredths). 


FORMULAS  327 

13.  The    amount   of    a    sum   of    money   may   be    obtained 
by  adding  the  principal  to  the  quantity  obtained  by  multi- 
plying the  principal,  the  time   (as  years),  and  the  rate   (as 
hundredths). 

14.  To  find  the  length  of  an  arc  of  a  circle :  Multiply  the 
diameter  of  the  circle  by  the  number  of  degrees  in  the  arc  and 
this  product  by  .0087266. 

15.  To.  find  the  area  of  a  sector  of  a  circle :  Multiply  the 
number  of  degrees  in  the  arc  of  the  sector  by  the  square  of  the 
radius  and  by  .008727;  or,  multiply  the  arc  of  the  sector  by 
half  its  radius. 

Translating  Formulas  into  Rules 

In  order  to  understand  a  formula,  it  is  necessary  to  be  able 
to  express  it  in  simple  language. 

1.  One  of  the  simplest  formulas  is  that  for  finding  the  area 
of  a  circle,  A  =  TT  R* 

Here  A  stands  for  the  area  of  a  circle, 

E  for  the  radius  of  the  circle. 

TT  is  a  constant  quantity  and  is  the  ratio  of  the  circumference  of  a 
circle  to  its  diameter.  The  exact  value  cannot  be  expressed  in  figures, 
but  for  ordinary  purposes  is  called  3.1416  or  3^. 

Therefore,  the  formula  reads,  the  area  of  a  circle  is  equal  to 
the  square  of  the  radius  multiplied  by  3.1416. 

2.  The  formula  for  finding  the  area  of  a  rectangle  is 

A  =  Lx  W 

Here  A  =  area  of  a  rectangle 
L  =  length  of  rectangle 
W  =  width  of  rectangle 

The  area  of  a  rectangle,  therefore,  is  found  by  multiplying 
the  length  by  the  width, 


328       VOCATIONAL  MATHEMATICS  FOR   GIRLS 

EXAMPLES 

Express  the  facts  of  the  following  formulas  as  rules : 

1.  Electromotive  force  or  voltage  of  electricity  delivered  by 
a  current,  when  current  and  resistance  are  given: 

E  =  RI 

2.  For  the  circumference  of  a  circle,  when  the  length  of  the 
radius  is  given: 

O   ^—  £  7T MV    OF    7T.L/ 

3.  For  the  area  of  an  equilateral  triangle,  when  the  length 
of  one  side  is  given:  a*v'3 

T~ 

4.  For  the  volume  of  a  circular  pillar,  when  the  radius  and 
height  are  given : 


5.  For  the  volume  of  a  square  pyramid,  when  the  height 
and  one  side  of  the  base  are  given  : 

o^ 
3 

6.  For  the  volume  of  a  sphere,  when  the  diameter  is  given  : 


7.   For  the  diagonal  of  a  rectangle,  when  the  length  and 
breadth  are  given  : 


8.  For  the  average  diameter  of  a  tree,  when  the  average 

girth  is  known  :  G 

Lf  =  — 

7T 

9.  For  the  diameter  of  a  ball,  when  the  volume  of  it  is 
known.  sf 


FORMULAS  329 

10.  The  diameter  of  a  circle  may  be  obtained  from  the  area 
by  the  following  formula : 

Z>  =  1.1283  x  VZ 

11.  The  number  of  miles  in   a  given  length,  expressed  in 
feet,  may  be  obtained  from  the  formula 

M  =  .00019  x  F 

12.  The  number  of  cubic  feet  in  a  given  volume  expressed 
in  gallons  may  be  obtained  from  the  formula 

C  =  .13367  x  O- 

13.  Contractors   express   excavations   in   cubic  yard  s ;   the 
number  of  bushels  in  a  given  excavation  expressed  in  yards 
may  be  obtained  from  the  formula 

C  =  .0495  x  Y 

14.  The  circumference  of  a  circle  may  be  obtained  from  the 
area  by  the  formula 

(7=  3.5446  x  V2 

15.  The  area  of  the  surface  of  a  cylinder  may  be  expressed 
by  the  formula  A  =  (C  X  L)  +  2a 

When  C  =  circumference 

L  =  length 
a  =  area  of  one  end 

16.  The  surface  of  a  sphere  may  be  expressed  by  the  formula 

S  =  D*  x  3.1416 

17.  The  solidity  of  a  sphere  may  be   obtained  from   the 
formula 

S  =  D3  X  .5236 

18.  The  side  of  an  inscribed  cube  of  a  sphere  may  be  ob- 
tained from  the  formula 

S  =  E*  1.1547,     where  S  =  length  of  side, 

It  =  radius  of  sphere. 


330       VOCATIONAL   MATHEMATICS   FOR   GIRLS 

19.  The  solidity  or  contents  of  a  pyramid  may  be  expressed 

by  the  formula 

-pi 

S  =  A  x  —  ,          where  A  =  area  of  base, 

F  =  height  of  pyramid. 

20.  The  length  of  an  arc  of  a  circle  may  be  obtained  from 
the  formula 

L  =  N  x  .017453  R,          where  L  =  length  of  arc, 

N  =  number  of  degrees, 
R  =  radius  of  circle. 

21.  The   loss  in   a  transaction    may    be   expressed   by    the 
formula 

L  =  c  x  r,  where  L  =  loss, 

c  =  cost, 
r  =  rate  of  loss. 

22.  The  rate  of  loss  in  a  transaction  may  be  expressed  by 
the  formula 


23.  The   cost  of  a  commodity  may   be   expressed   by   the 
formula 

or 

c  =  —  —  --  ,  where  S  =  selling  price, 

lUU  -r-  T 

C  =  COSt, 

r  =  rate. 

24.  The  volume  of  a  sphere  when  the  circumference  of  a 
great  circle  is  known  may  be  determined  by  the  formula 

v-C3  . 
~e^ 

25.  The  diameter  of  a  circle  the  circumference  of  which 
is  known  may  be  found  by  the  formula 


FORMULAS  331 

26.    The  area  of  a  circle  the  circumference  of  which  is  known 
may  be  found  by  the  formula 


Coefficients  and  Similar  Terms 

When  a  quantity  may  be  separated  into  two  factors,  one  of 
these  is  called  the  coefficient  of  the  other  ;  but  by  the  coefficient 
of  a  term  is  generally  meant  its  numerical  factor. 

Thus,  4  b  is  a  quantity  composed  of  two  factors  4  and  b  ;  4  is  a  coef- 
ficient of  b. 

Similar  terms  are  those  that  have  as  factors  the  same  letters 
with  the  same  exponents. 

Thus,  in  the  expression,  6  a,  4  b,  2  a,  5  a&,  5  a,  2  b.  6  a,  2  a,  5  a  are 
similar  terms  ;  46,  2b  are  similar  terms  ;  5  ab  and  6  a  are  not  similar 
terms  because  they  do  not  have  the  same  letters  as  factors.  3  ab,  5  ab, 
lab,  Sab  are  similar  terms.  They  may  be  united  or  added  by  simply 
adding  the  letters  to  the  numerical  sum,  17  ab. 

In  the  following,  8  6,  5  &,  3  ab,  4  a,  ab,  and  2  a,  8  b  and  5  b  are  similar 
terms  ;  3  ab  and  ab  are  similar  terms  ;  4  a  and  2  a  are  similar  terms  ;  8  b, 
3  ab,  and  4  a  are  dissimilar  terms. 

In  addition  the  numerical  coefficients  are  algebraically  added  ; 
in  subtraction  the  numerical  coefficients  are  algebraically  sub- 
tracted ;  in  multiplication  the  numerical  coefficients  are  alge- 
braically multiplied  ;  in  division  the  nurnerial  coefficients  are 
algebraically  divided. 

EXAMPLES 

State  the  similar  terms  in  the  following  expressions  : 

1.  5  a?,  8  ax,  3x,  2  ax.  6.    15  abc,  2  abc,  4  abc,  2  ab, 

2.  8  abc,  7c,  2ab,  3c,  Sab,     3a&. 

7.   8x,  6x,  13xy,  5x,  1  y. 

3.  2pq,  5p,  8  q,  2p,  3  q,  5pq.        8.    7y,2y,2  xy,  3y,2xy. 

4.  47/,  5yz,  2y,15z,5z,2yz. 


v 

_    ,  Q  9.   2  7T;  5  Trr2,  -,  Ti-r,  2  TTT. 

5.   18  mn,  6  m,  5  rc,  4  mw,  2m.  2 


332       VOCATIONAL  MATHEMATICS  FOR   GIRLS 

Equations 

A  statement  that  two  quantities  are  equal  may  be  expressed 
mathematically  by  placing  one  quantity  on  the  left  and  the 
other  on  the  right  of  the  equality  sign  (=).  The  statement 
in  this  form  is  called  an  equation. 

The  quantity  on  the  left  hand  of  the  equation  is  called  the 
left-hand  member  and  the  quantity  on  the  right  hand  of  the 
equation  is  called  the  right-hand  member. 

An  equation  may  be  considered  as  a  balance.  If  a  balance 
is  in  equilibrium,  we  may  add  or  subtract  or  multiply  or  divide 
the  weight  on  each  side  of  the  balance  by  the  same  weight  and 
the  equilibrium  will  still  exist.  So  in  an  equation  we  may 
perform  the  following  operations  on  each  member  without 
changing  the  value  of  the  equation : 

We  may  add  an  equal  quantity  or  equal  quantities  to  each  mem- 
ber of  the  equation. 

We  may  subtract  an  equal  quantity  or  equal  quantities  from 
each  member  of  the  equation. 

We  may  multiply  each  member  of  the  equation  by  the  same  or 
equal  quantities. 

We  may  divide  each  member  of  the  equation  by  the  same  or 
equal  quantities. 

We  may  extract  the  square  root  of  each  member  of  the  equation. 

We  may  raise  each  member  of  the  equation  to  the  same  power. 

The  expression,  A  =  trip  is  an  equation.     Why  ? 

If  we  desire  to  obtain  the  value  of  R  instead  of  A  we  may  do 
so  by  the  process  of  transformation  according  to  the  above 
rules.  To  obtain  the  value  of  R  means  that  a  series  of  opera- 
tions must  be  performed  on  the  equation  so  that  R  will  be  left 
on  one  side  of  the  equation. 

(1)  .A  =  irIP 

(2)  —  =  IP     (Dividing  equation  (1)  by  the  coefficient  of  .R2.) 

(3)  -/—  =  R     (Extracting  the  square  root  of  each  side  of  the  equation.) 


FORMULAS  333 

Methods  of  Representing  Operations 
MULTIPLICATION 

The  multiplication  sign  (  X )  is  used  in  most  cases.  It  should 
not  be  used  in  operations  where  the  letter  (x)  is  also  to  be  em- 
ployed. 

Another  method  is  as  follows  : 

2-3     a-6     2a-3b     4 x • 5  a 

This  method  is  very  convenient,  especially  where  a  number 
of  small  terms  are  employed.  Keep  the  dot  above  the  line, 
otherwise  it  is  a  decimal  point. 

Where  parentheses,  etc.,  are  used,  multiplication  signs  may 
be  omitted.  For  instance,  (a  +  b)  x  (a  —  b)  and  (a  +  &)(a  —  b) 
are  identical ;  also,  2  •  (x  —  y)  and  2(x  —y). 

The  multiplication  sign  is  very  often  omitted  in  order  to 
simplify  work.  To  illustrate,  2  a  means  2  times  a ;  5  xyz  means 
5  •  x  •  y  •  z ;  x(a  —  b)  means  x  times  (a  —  &),  etc. 

A  number  written  to  the  right  of,  and  above,  another  (x*~)  is 
a  sign  indicating  the  special  kind  of  multiplication  known  as 
involution. 

In  multiplication  we  add  exponents  of  similar  terms. 

Thus,  x2  -  y?  =  #2+3  =  x5 

abc  •  ab  •  «26  =  a4b3c 

The  multiplication  of  dissimilar  terms  may  be  indicated. 
Thus,  a  •  b  •  c  •  x  •  y  •  z  =  abcxyz. 

DIVISION 

The  division  sign  (-*-)  is  used  in  most  cases.  In  many 
cases,  however,  it  is  best  to  employ  a  horizontal  line  to  indicate 

division.     To  illustrate,  a          means  the  same  as  (a  +  &)  -f- 
x-y 

(x  —  y)  in  simpler  form.     The  division  sign  is  never  omitted. 


334       VOCATIONAL  MATHEMATICS  FOR   GIRLS 


A  root  or  radical  sign  (yH,  ^/x2)  is  a  sign  indicating  the  special 
form  of  division  known  as  evolution. 

In  division,  we  subtract  exponents  of  similar  terms. 

Thus,  y?  +  xi  =  —  =  y?-2  =  x 


The  division  of  dissimilar  terms  may  be  indicated. 


Thus, 

xyz 

Substituting  and  Transposing 

A  formula  is  usually  written  in  the  form  of  an  equation. 
The  left-hand  member  contains  only  one  quantity,  which  is 
the  quantity  that  we  desire  to  find.  The  right-hand  member 
contains  the  letters  representing  the  quantity  and  numbers 
whose  values  we  are  given  either  directly  or  indirectly. 

To  find  the  value  of  the  formula  we  must  (1)  substitute  for 
every  letter  in  the  right-hand  member  its  exact  numerical 
value,  (2)  carry  out  the  various  operations  indicated,  remem- 
bering to  perform  all  the  operations  of  multiplication  and 
division  before  those  of  addition  and  subtraction,  (3)  if  there 
are  any  parentheses,  these  should  be  removed,  one  pair  at  a 
time,  inner  parentheses  first.  A  minus  sign  before  a  parenthesis 
means  that  when  the  parenthesis  is  removed,  all  the  signs  of 
the  terms  included  in  the  parenthesis  must  be  changed. 

Find  the  value  of  the  expression 

3a  +  6(2a-&  +  18),  where  a  =  5,  b  =  3. 

Substitute  the  value  of  each  letter.  Then  perform  all  addition  or 
subtraction  in  the  parentheses. 

3x5  +  3(10  -3  +  18) 
15  +  3(28-3) 
15  +  3(25) 
15  +  75  =  90 


FORMULAS  335 

EXAMPLES 

Find  the  value  of  the  following  expressions : 

1.  2  A  x  (2  +  3  A)  X  8,  when  A  =  10. 

2.  8  a  X  (6  —  2  a)  X  7,  when  a  =  7. 

4.  8  (a?  +  y),  when  x  =  9 ;  y  =  11. 

5.  13  (a;—  y),  when  x  =  27  ;  y  =  9. 

6.  24  y  -f  8  z  (2  +  y)  —  3  y,  when  ?/  =  8 ;  2  =  11. 

7.  Q(6  Jf +3^r)-f2  0,  when  M  =  4,  ^=5,  Q  =  6,  0  =  8. 

8.  Find  the  value  of  X  in  the  formula  X  = 
when  Jf  =  11,  N=  9,  P  =  28. 

9.  5 


P—  Q 

10.   Find  the  value  of  T  in  the  equation 


11.  3  a  -f-  4  (6  —  2  a  +  3  c)  —  c,  when  a  =  4,  6  =  6,  c  =  2. 

12.  5|>  —  8  q  (p  4-  r  —  $)  —  g,  when  p  =  5,  g  =  7,  r  =  9,  $  =  11. 

13.  si  +  p  —  p^  —  S^  +  t+p),  when  p  =  5,  S  =  8,  t  =  9. 

14.  a2  —  63  -\-  c2,  when  a  =  9,  6  =  6,  c  =  4. 

15.  (a  +  6)  (a  +  6  —  c),  when  a  =  2,  6  =  3,  c  =  4. 

16.  (a2 -62)  (a2 +  62),  when  a  =  8,  6  =  4. 

17.  (c3  +  d3)  (c3  -  d3),  c  =  9,  d  =  5. 

18.  Va2  +  2  a6  +  62,  when  a  =  7,  6  =  8. 

19.  "v/c3  —  61,  when  c  =  5. 


336       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

PROBLEMS 

Solve  the  following  problems  by  first  writing  the  formula 
from  the  rule  on  page  326,  and  then  substituting  for  the  answer. 

1.  How  many  electrical  horse  power  in  4389  watts  ? 

2.  How  many  kilowatts  in  2389  watts  ? 

3.  (a)  Give  the  number  of  watts  in  a  circuit  of  110  volts 
and  25  amperes. 

(b)  How  many  electrical  horse  power  ? 

4.  What  is  the  voltage  of  a  circuit  if  the  horse  power  is 
2740  watts  and   the   quantity  of   electricity   delivered   is   25 
amperes  ? 

5.  What  is  the  resistance  of  a  circuit  if  the  voltage  is  110 
and  the  quantity  of  electricity  is  25  amperes  ? 

6.  What  is  the  pressure  per  square  inch  of  water  87  feet 
high? 

7.  What  is  the  capacity  of  a  cylinder  with  a  base  of  16 
square  inches  and  6   inches   high?     (Capacity  in   gallons   is 
equal  to  cubical  contents  obtained  by  multiplying  base  by  the 
height  and  dividing  by  231  cubic  inches.) 

8.  What  is  the  length  of  a  30°  arc  of  a  circle  with  16" 
diameter  ? 

9.  What  is  the  area  of  a  sector  which  contains  an  arc  of 
40°  in  a  circle  of  diameter  18"  ? 

10.  What  is  the  amount  of  $  800  at  the  end  of  5  years  at  5  %  ? 

11.  What  is  the  amount  of  gain  in  a  transaction,  when  a 
man  buys  a  house  for  $  5000  and  gains  10  %  ? 

12.  What  is  the  selling  price  of  an   automobile  that   cost 
$  895,  if  the  salesman  gained  33  %  ? 

13.  What  is  the  capacity  of  a  pail  14"  (diameter  of  top), 
11"  (diameter  of  bottom),  and  16"  in  height  ? 

14.  What  is  the  area  of  an  ellipse  with  the  greatest  length 
16"  and  the  greatest  breadth  10"  ? 


FORMULAS 


337 


Interpretation  of  Negative  Quantities 

The  quantity  or  number  —  12  has  no  meaning  to  us  according 
to  our  knowledge  of  simple  arithmetic,  but  in  a  great  many 
problems  in  practical  work  the  minus  sign  before  a  number 
assists  us  in  understanding  the  different  solutions. 

To  illustrate : 


FAHRENHEIT  THF.BMOMETEB 


CENTIGRADE  THERMOMETER 


Boiling 
point  of 
water 


Freezing 
point  of  • 
water 


212° 


Boiling 
point  of 
water 


§•§<! 


-32° 


Freezing 
point  of  • 
water 


100° 


-0° 


On  the  Centigrade  scale  the  freezing  point  of  water  is  marked 
0°.  Below  the  freezing  point  of  water  on  the  Centigrade  scale 
all  readings  are  expressed  as  minus  readings. 

—  30°  C  means  thirty  degrees  below  the  freezing  point.  In 
other  words,  all  readings,  in  the  direction  below  zero  are 
expressed  as  — ,  and  all  readings  above  zero  are  called  +. 
Terms  are  quantities  connected  by  a  p'lus  or  minus  sign. 
Those  preceded  by  a  plus  sign  (when  no  sign  precedes  a  quan- 
tity plus  is  understood)  are  called  positive  quantities,  while 
those  connected  by  a  minus  sign  are  called  negative  quantities. 


338       VOCATIONAL  MATHEMATICS  FOR   GIRLS 

Let  us  try  some  problems  involving  negative  quantities. 
Find  the  corresponding  reading  on  the  Fahrenheit  scale  cor~ 
responding  to  — 18°  C. 

F  =  §  C  +  32° 

F  =  f(-  18°) +.32° 

Notice  that  a  minus  quantity  is  placed  in  parenthesis  when  it  is  to  be 
multiplied  by  another  quantity. 

F  =-  ip>  +  32°  =  -  32f°  +  32°  ;  F  =-  |°. 

The  value  —  f  °  is  explained  by  saying  it  is  f  of  a  degree  below  zero 
point  on  Fahrenheit  scale. 

Let  us  consider  another  problem.  Find  the  reading  on  the  Centi- 
grade scale  corresponding  to  —  40°  F. 

Substituting  in  the  formula,  we  have 

C  =  I  (_  40°  -  32°)  =  |  (-  72°)  =  -  40°. 

Since  subtracting  a  negative  number  is  equivalent  to  adding 
a  positive  number  of  the  same  value,  and  subtracting  a  posi- 
tive number  is  equivalent  to  adding  a  negative  number  of  the 
same  value,  the  rule  for  subtracting  may  be  expressed  as  fol- 
lows :  Change  the  sign  of  the  subtrahend  and  proceed  as  in 
addition. 

For  example,  40  minus  —  28  equals  40  plus  28,  or  68. 

40  minus  +  28  equals  40  plus  —  28,  or  12. 

—  40  minus  +  32  equals  —  40  plus  —  32  =  -  72. 

(Notice  that  a  positive  quantity  multiplied  by  a  negative  quantity  or 
a  negative  quantity  multiplied  by  a  positive  quantity  always  gives  a 
negative  product.  Two  positive  quantities  multiplied  together  will  give 
a  positive  product,  and  two  negative  quantities  multiplied  together  will 
give  a  positive  product. )  To  illustrate  : 

5  times  5  =  5  x  5  =  25 

5  times  _  5  =£  x(- 5)  =  -26 

(-5)  times  (-5)  =  +25 

In  adding  positive  and  negative  quantities,  first  add  all  the 
positive  quantities  and  then  add  all  the  negative  quantities 


FORMULAS  339 

together.     Subtract  the  smaller  from  the  larger  and  prefix  the 
same  sign  before  the  remainder  as  is  before  the  larger  number. 

For  example,  add  : 

2  a,  5  a,  —  6  a,  8  a,  -  2  a 
2a  +  5a-f  8a  =  15a  ;  —  Qa-2a  =  -Ba 
15  a  —  8  a  =  7  a 

EXAMPLES 

Add  the  following  terms  : 

1.  3  x,  —  x,  1  x,  4  Xj  —  '2  x. 

2.  6y,  2y,  9y,  -7y. 

3.  9  ab,  2  db,  6  ab,  -  4  a&,  7  a&,  -  5  a&. 

Multiplication  of  Algebraic  Expressions 

Each  term  of  an  algebraic  expression  is  composed  of  one  or 
more  factors,  as,  for  example,  2  ab  contains  the  factors  #,  a,  and 
b.  The  factors  of  a  term  have,  either  expressed  or  understood, 
a  small  letter  or  number  in  the  upper  right-hand  corner,  which 
states  how  many  times  the  quantity  is  to  be  used  as  a  factor. 
For  instance,  ab2.  The  factor  a  has  the  exponent  1  understood 
and  the  factor  b  has  the  exponent  2  expressed,  meaning  that  a 
is  to  be  used  once  and  b  twice  as  a  factor.  abz  means,  then, 
a  X  b  X  b.  The  rule  of  algebraic  multiplication  by  terms  is  as 
follows:  Add  the  exponents  of  all  like  letters  in  the  terms 
multiplied  and  use  the  result  as  exponent  of  that  letter  in  the 
product.  Multiplication  of  unlike  letters  may  be  expressed 
by  placing  the  letters  side  by  side  in  the  product. 


For  example  :  2  ab  x  3  &2  = 

4  a  x  3  b  =  12  ab 

Algebraic  or  literal  expressions  of  more  than  one  term  are 
multiplied  in  the  following  way  :  begin  with  the  first  term  to 
the  left  in  the  multiplier  and  multiply  every  term  in  the  multi- 
plicand, placing  the  partial  products  underneath  the  line.  Then 


340       VOCATIONAL  MATHEMATICS  FOR   GIRLS 

repeat  the  same  operation,  using  the  second  term  in  the  multi- 
plier. Place  similar  products  of  the  same  factors  and  degree 
(same  exponents)  in  same  column.  Add  the  partial  products. 

Thus,  a  +  b  multiplied  by  a  —  b. 

a  +  b 
a-b 


a?+  ab  -  62 

-ab 
a2  -62 

Notice  the  product  of  the  sum  and  difference  of  the  quantities  is  equal 
to  the  difference  of  their  squares. 

EXAMPLES 

1.  Multiply  a  -f-  b  by  a  +  b. 

State  what  the  square  of  the  sum  of  the  quantities  equals. 

2.  Multiply  x  —  y  by  x  —  y. 

State  what  the  square  of  the  difference  of  the  quantities  equals. 

3.  Multiply  (p  +  q)(p  —  q).  7.   Multiply  (a;  —  y)(x  —  y). 

4.  Multiply  (p  +  g)(jp  +  g).  8.   (x  +  2/)2=? 

5.  Multiply  (r  -f  s)(r  -  s).  9.    (a;  -  y)2  =  ? 

6.  Multiply  (a  ±  6)(a  ±  b).  10.   (x  +  y)(x  -  y)  =  ? 


USEFUL  MECHANICAL  INFORMATION 

There  are  certain  mechanical  terms  and  laws  that  every  girl 
should  know  and  be  able  to  apply  to  the  labor-saving  devices 
and  machines  that  are  used  in  the  home  to-day. 

Time  and  Speed 

Two  important  terms  are  time  and  speed.  Speed  is  the 
name  given  to  the  time-rate  of  change  of  position.  That  is, 

Sueed  —  Change  of  position  or  distance 
Time  taken 

EXAMPLES 

1.  A  train  takes  120  seconds  to  go  one  mile ;  what  is  its 
speed  in  miles  per  hour  ? 

One  hour  contains  60  minutes,  1  minute  contains  60  seconds,  then  1  hour 
contains 

60  x  60  =  3600  seconds. 

If  the  train  goes  one  mile  in  120  seconds,  in  one  second  it  will  go  T£7 
of  a  mile  and  in  3600  seconds  it  will  go 

3600  x  T£7  =  30  miles  per  hour.   Ans. 

2.  At  the  rate  of  80  seconds  per  mile,  how  fast  is  a  train 
moving  in  miles  per  hour  ? 

In  a  second  it  will  move  ^  of  a  mile  ;  in  3600  seconds  it  will  move 
3600  times  as  much. 

3.  At  the  rate  of  55  miles  an  hour,  how  many  seconds  will 
it  require  to  travel  between  mile-posts  ? 

4.  A  watch  shows  55  seconds  between  mile-posts  ;  what  is 
the  speed  in  miles  per  hour  ? 

341 


342        VOCATIONAL  MATHEMATICS   FOR   GIRLS 

5.  What  number  of  seconds  between  mile-posts  will  corre- 
spond to  a  speed  of  40  miles  an  hour  ? 

6.  The  rim  of  a  fly-wheel  is  moving  at  the  rate  of  one  mile 
a  minute.     How  many  feet  does  it  move  in  a  second  ? 

7.  If  a  train  continues  to  travel  at  the  rate  of  44  feet  a 
second,  how  many  miles  will  it  travel  in  an  hour  ? 

8.  If  a  train  travels  at  the  rate  of  3.87  miles  in  6  minutes, 
how  many  miles  an  hour  is  it  traveling  ? 

Motion  and  Momentum 

Many  interesting  facts  about  the  motion  of  bodies  can  be 
understood  by  the  aid  of  a  knowledge  of  the  laws  of  motion 
and  momentum. 

A  body  acted  upon  by  some  force,1  such  as  steam  or  elec- 
tricity, starts  slowly,  increasing  its  speed  under  the  action  of 
the  force.  To  illustrate :  —  when  an  electric  car  starts,  we 
often  experience  a  heavy  jarring ;  this  is  due  to  the  fact  that 
the  seat  starts  before  our  body,  and  the  seat  pushes  us  along. 
There  is  a  tendency  of  bodies  to  remain  in  a  state  of  rest  or 
motion,  which  is  called  inertia,  that  is,  the  inability  of  a  body 
itself  to  change  its  position,  to  stop  itself  if  moving,  or  to  start 
if  at  rest. 

The  momentum  of  a  body  is  defined  as  the  quantity  of 
motion  in  a  body,  and  is  the  product  of  the  mass2  and  the 
velocity  in  feet  per  second  (speed). 

EXAMPLE.  To  find  the  momentum  of  a  body  9  pounds  in 
weight,  when  moving  with  the  velocity  of  75  feet  per  second. 

If  the  mass  of  the  body  upon  which  the  force  acts  is  given  in  pounds, 
and  the  velocity  in  seconds,  the  force  will  be  given  in  foot-pounds. 

MASS  VELOCITY  MOMENTUM 

9  x  75  675  foot-pounds. 

1  Force  is  that  which  tends  to  produce  motion. 

2  Mass  is  the  quantity  of  matter  in  a  body. 


USEFUL  MECHANICAL  INFORMATION  343 

We  may  abbreviate  this  rule  by  allowing  letters  to  stand  for 
quantities.  Let  the  mass  be  represented  by  M  and  the  veloc- 
ity by  V. 

EXAMPLES 

1.  What  is  the  momentum  of  a  car  weighing  15  tons,  mov- 
ing 12  miles  per  hour  ? 

2.  What  is  the  momentum  of  a  motor-car  weighing  3  tons, 
moving  26  miles  per  hour  ? 

3.  What  is  the  momentum  of  a  person  weighing  135  pounds, 
moving  5  miles  per  hour  ? 

4.  A  truck  weighing  4  tons  has  a  momentum  of  520,000  foot- 
pounds.    At  what  speed  is  it  moving  ? 

Work  and  Energy 

Work  is  the  overcoming  of  resistance  of  any  kind.  Energy 
is  the  ability  to  do  work.  Work  is  measured  in  a  unit  called 
a  foot-pound.  It  is  the  work  done  in  raising  one  pound  one 
foot  in  one  second.  One  horse  power  is  33,000  foot-pounds  in 
one  minute. 

EXAMPLES 

1.  A  woman  lifts  a  package  weighing  15  Ib.  from  the  floor 
to  a  shelf  5  ft.  above  the  floor  in  two  seconds.     How  many 
foot-pounds  of  force  does  she  use  ? 

2.  How  much  work  does  a  woman  weighing  130  pounds  do 
in  climbing  a  13-story  building  in  20  minutes  ?     Each  story 
is  16'  high. 

3.  If  an  engine  is  rated  at  5  H.  P.,1  how  much  work  will  it 
do  in  8  seconds  ?  in  3  minutes  ? 

1  Remember  that  1  H.  P.  means  33,000  ft.-lb.  in  one  minute. 


344       VOCATIONAL  MATHEMATICS   FOR   GIRLS 

4.  Find  the  horse  power  developed  by  a  locomotive  when  it 
draws  at  the  rate  of  31  miles  per  hour  a  train  offering  a  resist- 
ance of  130,000  Ib. 

Machines 

Experience  shows  that  it  is  often  possible  to  use  our  strength 
to  better  advantage  by  means  of  a  contiivance  called  a 
machine.  Every  home-maker  is  interested  in  labor-saving 
devices. 

The  mechanical  principles  of  all  simple  machines  may  be 
resolved  into  those  of  the  lever,  including  the  wheel  and  axle 
and  pulley,  and  the  inclined  plane,  to  which  belong  the  wedge 
and  screw. 

In  all  machines  there  is  more  or  less  friction.1  The  work 
done  by  the  acting  force  always  exceeds  the  actual  work 
accomplished  by  the  amount  that  is  transformed  into  heat. 
The  ratio  of  the  useful  work  to  the  total  work  done  by  the 
acting  force  is  called  the  efficiency  of  the  machine. 


Em  i          —  ^se^  work  accomplished  ^ 
Total  work  expended 

•  Levers.  —  The  efficiency  of  simple  levers  is  very  nearly 
100  %  because  the  friction  is  so  small  as  to  be  disregarded. 

Inclined  Planes.  —  In  the  inclined  plane  the  friction  is 
greater  than  in  the  lever,  because  there  is  more  surface  with 
which  the  two  bodies  come  in  contact  ;  the  efficiency  is  some- 
where between  90  %  and  100  %  . 

Pulleys.  —  The  efficiency  of  the  commercial  block  and  tackle 
with  several  movable  pulleys  varies  from  40  %  to  60  %  . 

Jack  Screw.  —  In  the  use  of  the  jack  screw  there  is  neces- 
sarily a  very  large  amount  of  friction  so  that  the  efficiency  is 
often  as  low  as  25  %. 

1  Friction  is  the  resistance  which  every  material  surface  offers  to  the  slid- 
ing or  moving  of  any  other  surface  upon  it. 


USEFUL  MECHANICAL  INFORMATION          345 

EXAMPLES 

1.  Mention  some  instances  in  which  friction  is  of  advantage. 

2.  If  472  foot-pounds  of  work  are  expended  by  a  dredge  in 
raising  a  load,  and  only  398  pounds  of  useful  work  are  accom- 
plished, what  is  the  efficiency  of  the  dredge  ? 

3.  If  250  foot-pounds  of  work  are  expended  at  one  end  of 
a  lever,  and  249  pounds  of  useful  work  are  accomplished,  what 
is  the  efficiency  of  the  lever  ? 

4.  If  589  foot-pounds  of  work  are  expended  in  raising  a 
body  on  an   inclined  plane,  and   only  584  pounds  of   useful 
work  are  accomplished,  what  is  the  efficiency  of  the  inclined 
plane  ? 

5.  If  844  foot-pounds  of   work  are  expended  in  raising   a 
body  by  means  of  pulleys  and  only  512  pounds  of  useful  work 
are  accomplished,  what  is  the  efficiency  of  the  pulley  ? 

Water  Supply 

The  question  of  the  water  supply  of  a  city  or  a  town  is  very 
important.  Water  is  usually  obtained  from  lakes  and  rivers 
which  drain  the  surrounding  country.  If  a  lake  is  located  in 
a  section  of  the  surrounding  country  higher  than  the  city 
(which  is  often  located  in  a  valley),  the  water  may  be  obtained 
from  the  lake,  and  the  pressure  of  the  water  in  the  lake  may 
be  sufficient  to  force  it  through  the  pipes  into  the  houses.  But 
in  most  cases  a  reservoir  is  built  at  an  elevation  as  high  as  the 
highest  portion  of  the  town  or  city,  and  the  water  is  pumped 
into  it.  Since  the  reservoir  is  as  high  as  the  highest  point  of 
the  town,  the  water  will  flow  from  it  to  any  part  of  the  town. 
If  houses  are  built  on  the  same  hill  with  the  reservoir,  a  stand- 
pipe,  which  is  a  steel  tank,  is  erected  on  this  hill  and  the  water 
is  pumped  into  it. 

Water  is  conveyed  from  the  reservoir  to  the  house  by  means 


346       VOCATIONAL  MATHEMATICS   FOR   GIRLS 


of  iron  pipes  of  various  sizes.  It  is  distributed  to  the  differ- 
ent parts  of  the  house  by  small  lead,  iron,  or  brass  pipes. 
Since  water  exerts  considerable  pressure,  it  is  necessary  to 
know  how  to  calculate  the  exact  pressure  in  order  to  have  pipes 
of  proper  size  and  strength. 


WATER  SUPPLY 
The  distribution  of  water  in  a  city  during  1912  is  as  follows 


MONTHS 

» 

w 
~  _ 

O 

GALLONS  PHR 
DAY 

ESTIMATED  No. 
OF  CONSUMERS 

POPULATION 

GALLONS  PER 
DAY  FOR  EACH 
CONSUMER 

GALLONS  PER 
DAY  FOR  EACH 
INHABITANT 

January    . 

157,866,290 

5,092,461 

February  . 

147,692,464 

5,092,844 

March  . 

146,933,054 

4,739,776 

April   . 

143,066,067 

4,768,869 

May     .     . 

161,177,486 

5,199,274 

o 

r-  1 

o 

June    .     . 

176,479,354 

5,882,645 

O 

"^ 

July     .     . 

189,063,250 

6,098,815 

1—  1 

^ 

August 

179,379,566 

5,786,438 

September 

169,394,758 

5,646,492 

October    . 

176,067,571 

5,679,599 

November 

153,484,712 

5,116,157 

December 

151,976,208 

4,902,458 

What  is  the  number  of  gallons  per  day  for  each  consumer  ? 
What  is  the  number  of  gallons  per  day  for  each  inhabitant  ? 


PLUMBING  AND  HYDRAULICS  347 

EXAMPLES 

1.  Water  is  measured  by  means  of   a  meter.     If  a  water 
meter  measures  for  live  hours  760  cubic  feet,  how  many  gal- 
lons does  it  indicate  ? 

NOTE.  — 231  cubic  inches  =  1  gallon. 

2.  If  a  water  meter  registered  1845  cubic  feet  for  3  days, 
how  many  gallons  were  used  ? 

3.  A  tank  holds  exactly  12,852  gallons  ;  what  is  the  capacity 
of  the  tank  in  cubic  feet  ? 

4.  A  tank  holds  3841  gallons  and  measures  4  feet  square  on 
the  bottom  ;  how  high  is  .the  tank  ? 

Rectangular  Tanks.  —  To  find  the  contents  in  gallons  of  a  square  or 
rectangular  tank,  multiply  together  the  length,  breadth,  and  height  in 
feet;  multiply  the  result  by  7.48. 

I  =  length  of  tank  in  feet 
b  =  breadth  of  tank  in  feet 
h  =  height  of  tank  in  feet 
Contents  =  Ibh  cubic  feet  x  7.48  =  7.48  Ibh 
gallons 

(NOTE.  —  1  cu.  ft.  =  7.48  gallons.) 

If  the   dimensions  of   the   tank  are  in  inches,  multiply  the  length, 
breadth,  and  height  together,  and  the  result  by  .004329. 

5.  Find  the  contents  in  gallons  of  a  rectangular  tank  having  in- 
side dimensions  (a)  12'  x  8'  x  8';  (b)  15"  x  11"  x  6" ;  (c)  3'  4" 
X  2'  8"  x  8";  (d)  5'  8"  x  4'  3"  x  3'  5" ;  (e)  3'  S"  x  3'  9"  x  2'  5". 

Cylindrical  Tank.  —  To  find  the  contents  of  a  cylin- 
drical tank,  square  the  diameter  in  inches,  multiply 
this  by  the  height  in  inches,  and  the  result  by  .0034. 

d  =  diameter  of  cylinder 
h  =  height  of  cylinder 
Contents  =  d2h  cubic  inches  x  .0034  =  d?h  .0034  gallons 


6.    Find  the  capacity  in  gallons  of  a  cylindrical  tank  (a)  14" 
in  diameter  and   8'  high;    (&)  6"  in  diameter  and   5'   high; 


348        VOCATIONAL  MATHEMATICS  FOR   GIRLS 

(c)  15"  in  diameter  and  4'  high;    (d)  V  8"  in  diameter  and 
5'  4"  high ;  (e)  2'  2"  in  diameter  and  6'  1"  high. 

Inside  Area  of  Tanks. — To  find  the  area,  for  lining  purposes,  of  a 
square  or  rectangular  tank,  add  together  the  widths  of  the  four  sides  of 
the  tank,  and  multiply  the  result  by  the  height.  Then  add  to  the  above 
the  area  of  the  bottom.  Since  the  top  is  usually  open,  we  do  not  line 
it.  In  the  following  problems  find  the  area  of  the  sides  and  bottom. 

7.  Find  the  amount  of  zinc  necessary  to  line  a  tank  whose 
inside  dimensions  are  2'  4"x  10"  x  10". 

8.  Find  the  amount   of   copper  necessary  to   line  a  tank 
whose  inside  dimensions  are  1'9"  x  11"  X  10",  no  allowance 
made  for  overlapping. 

9.  Find  the  amount   of   copper  necessary  to  line  a  tank 
whose  inside  dimensions  are  3'  4"  x  1'  2"  x  11",  no  allowance 
for  overlapping. 

10.  Find  the  amount  of  zinc  necessary  to  line  a  tank 
2'  11"  x  V  4"  x  10". 

Capacity  of  Pipes 

Law  of  Squares.  —  The  areas  of  similar  figures  vary  as  the 
squares  of  their  corresponding  dimensions. 

Pipes  are  cylindrical  in  shape  and  are,  therefore,  similar 
figures.  The  areas  of  any  two  pipes  are  to  each  other  as  the 
squares  of  the  diameters. 

EXAMPLE.  —  If  one  pipe  is  4"  in  diameter  and  another  is  2" 
in  diameter,  their  ratio  is  -^,  and  the  area  of  the  larger  one  is, 
therefore,  4  times  the  smaller  one. 

EXAMPLES 

1.  How  much  larger  is  a  section  of  5"  pipe  than  a  section 
of  2"  pipe  ? 

2.  How  much  larger  is  a  section  of  2±ff  pipe  than  a  section 
of  1"  pipe  ? 

3.  How  much  larger  is  a  section  of  5"  pipe  than  a  section  of 
3"  pipe  ? 


PLUMBING  AND   HYDRAULICS 


349 


Atmospheric  Pressure 

The  atmosphere  has  weight  and  exerts  .pressure.  The  pres- 
sure is  greatest  at  sea  level,  because  here  the  depth  of  the 
atmosphere  is  greatest.  In  mathematics  the  pressure  at  sea 
level  is  taken  as  the  standard.  Men  have  learned  to  make 
use  of  the  principles  of  atmospheric  pressure  in  such  devices 
as  the  pump,  the  barometer,  the  vacuum,  etc. 

Atmospheric   pressure   is  often   expressed  as   a 

certain  number  of  "  atmospheres."     The  pressure 

of  one  "  atmosphere  "  is  the  weight  of  a  column  of 

air,  one  square  inch  in  area. 
At  sea   level  the 

average  pressure  of 

the    atmosphere    is 

approximately   15 

pounds   per    square 

inch. 

The    pressure    of 

the  air  is  measured 

by    an     instrument 

called  a  barometer. 

The  barometer  con- 
sists of  a  glass  tube, 

about     311    inches 

long,      which      has 

been  entirely  filled 

with  mercury  (thus 

removing   all   air  from  the  tube)  and  inverted  in 

a  vessel  of  mercury. 

The  space  at  the  top  of  the  column  of  mercury 

varies  as  the  air  pressure  on  the  surface  of   the 

mercury  in  the  vessel  increases  or  decreases.     The 
BAROMETER  pressure  is  read  from  a  graduated  scale  which  indi- 


BAROMETER  TUBE 


350       VOCATIONAL  MATHEMATICS  FOR   GIRLS 

cates  the   distance  from  the   surface  of   the  mercury  in  the 
vessel  to  the  top  of  the  mercury  column  in  the  tube. 

QUESTIONS 

1.  Four  atmospheres  would  mean  how  many  pounds  ? 

2.  Give  in  pounds  the  following  pressures:  1  atmosphere; 
-J  atmosphere ;  J  atmosphere. 

3.  If   the   air,  on  the   average,  will   support  a  column  of 
mercury  30  inches  high  with  a  base  of  1  square  inch,  what 
is  the  pressure  of  the  air  ?     (One  cubic  foot  of  mercury  weighs 
849  pounds.) 

Water  Pressure 

When  water  is  stored  in  a  tank,  it  exerts  pressure  against 
the  sides,  whether  the  sides  are  vertical,  oblique,  or  horizontal. 
The  force  is  exerted  perpendicularly  to  the  surface  on  which  it 
acts.  In  other  words,  every  pound  of  water  in  a  tank,  at  a 
height  above  the  point  where  the  water  is  to  be  used,  possesses 
a  certain  amount  of  energy  due  to  its  position. 

It  is  often  necessary  to  estimate  the  energy  in  the  tank  at 
the  top  of  a  house  or  in  the  reservoir  of  a  town  or  city,  so  as 
to  secure  the  needed  water  pressure  for  use  in  case  of  fire.  In 
such  problems  one  must  know  the  perpendicular  height  from 
the  water  level  in  the  reservoir  to  the  point  of  discharge.  This 
perpendicular  height  is  called  the  head. 

Pressure  per  Square  Inch.  —  To  find  the  pressure  per  square 
inch  exerted  by  a  column  of  water,  multiply  the  head  of  water 
in  feet  by  0.434.  The  result  will  be  the  pressure  in  pounds. 

The  pressure  per  square  inch  is  due  to  the  weight  of  a  column  of 
water  1  square  inch  in  area  and  the  height  of  the  column.  Therefore, 
the  pressure,  or  weight  per  square  inch,  is  equal  to  the  weight  of  a  foot  of 
water  with  a  base  of  1  square  inch  multiplied  by  the  height  in  feet.  Since 
the  weight  of  a  column  of  water  1  foot  high  and  having  a  base  of  1  square 
inch  is  0.434  lb.,  we  obtain  the  pressure  per  square  inch  by  multiply- 
ing the  height  in  feet  by  0.434. 


PLUMBING  AND  HYDRAULICS 


351 


EXAMPLES 

What  is  the  pressure  per  square  inch  of  a  column  of  water 
(a)  8'  high?  (6)  15' 8"  high?  (c)  30' 4"  high?  (d)  18' 9" 
high  ?  (e)  41'  3"  high  ? 

Head.  —  To  find  the  head  of  water  in  feet,  if  the  pressure 
(weight)  per  square  inch  is  known,  multiply  the  pressure  by 
2.31. 

Let  p  =  pressure 

h  =  height  in  feet 
Then  p  =  h  x  0.434  Ib.  per  sq.  in. 


h  —    P     — 
~  0.434  ~  0.434 


X  p= 


EXAMPLES 

Find  the  head  of  water,  if  the  pressure  is  (a)  49  Ib.  per 
sq.  in. ;  (b)  88  Ib.  per  sq.  in. ;  (c)  46  Ib.  per  sq.  in. ;  (d) 
28  Ib.  per  sq.  in. ;  (e)  64  Ib.  per  sq.  in. 

Lateral  Pressure.  —  To  find  the  lateral 
(sideways)  pressure  of  water  upon  the 
sides  of  a  tank,  multiply  the  area  of  the 
submerged  side,  in  inches,  by  the  pressure 
due  to  one  half  the  depth. 

EXAMPLE.  —  A  tank  18"  long  and  12" 
deep  is  full  of  water.  What  is  the  lateral 
pressure  on  one  side  ? 


length        depth 

18"    x    12"    =  216  square  inches  =  area  of  side 

depth 

1'       X  0.434  =  .434  Ib.  pressure  at  the  bottom  of 

the  tank 

0  =  pressure  at  top 
2).4341b. 

.217  Ib.  average  pressure  due  to  one  half  the 

depth  of  the  tank 

.217  x  216  =  46.872  pounds  =  pressure  on  one 
side  of  the  tank 


— Pressure 
is  zero 


Pressure 

is  ha  If  that  at 
base 


LATERAL  PRESSURE 


352       VOCATIONAL  MATHEMATICS  FOR   GIRLS 


Water  Traps 

The  question  of  disposing  of  the  waste  water,  called  sewage,  is  of 
great  importance.  Various  devices  may  be  used  to  prevent  odors  from 
the  sewage  entering  the  house.  In  order  to  prevent  the  escape  of  gas 


WATER  TRAPS 

from  the  outlet  of  the  sewer  in  the  basement  of  a  house  or  building,  a 
device  called  a  trap  is  used.  This  trap  consists  of  a  vessel  of  water 
placed  in  the  waste  pipe  of  the  plumbing  fixtures.  It  allows  the  free  pas- 
sage of  waste  material,  but  prevents  sewer  gases  or  foul  odors  from  enter- 
ing the  living  rooms.  The  vessels  holding  the  water  have  different  forms ; 
(see  illustration) .  These  traps  may  be  emptied  by  back  pressure  or  by 
siphon.  It  is  a  good  plan  to  have  sufficient  water  in  the  trap  so  that  it 
will  never  be  empty.  All  these  problems  belong  to  the  plumber  and  in- 
volve more  or  less  arithmetic. 

To  determine  the  pressure  which  the  seal  of  a  trap  will  resist : 
EXAMPLE.  —  What  pressure  will  a  l^-inch  trap  resist  ? 

If  one  arm  of  the  trap  has  a  seal  of  If  inches,  both  arms  will  make  a 
column  twice  as  high,  or  3  inches.  Since  a  column  of  water  28  inches 
in  height  is  equivalent  to  a  pressure  of  1  pound,  or  16  ounces,  a  column 
of  water  1  inch  in  height  is  equivalent  to  a  pressure  of  $  of  a  pound,  or 
£|  =  £  ounces,  and  a  column  of  water  3  inches  in  height  is  equivalent  to 
3  x  |  =  ty  =  1.7  ounces. 

Therefore,  a  1^-inch  trap  will  resist  1.7  ounces  of  pressure. 


PLUMBING   AND   HYDRAULICS  353 

EXAMPLES 

1.  What  back  pressure  will  a  f-inch  seal  trap  resist  ? 

2.  What  back  pressure  will  a  2-inch  seal  trap  resist  ? 

3.  What  back  pressure  will  a  21-inch  seal  trap  resist  ? 

4.  What  back  pressure  will  a  4J-inch  seal  trap  resist  ? 

5.  What  back  pressure  will  a  5-inch  seal  trap  resist  ? 

Water  Power 

When  water  flows  from  one  level  to  another,  it  exerts  a 
certain  amount  of  energy,  which  is  the  capacity  for  doing 
work.  Consequently,  water  may  be  utilized  to  create  power 
by  the  use  of  such  means  as  the  water  wheel,  the  turbine,  and 
the  hydraulic  ram. 

Friction,  which  must  be  considered  when  one  speaks  of 
water  power,  is  the  resistance  which  a  substance  encounters 
when  moving  through  or  over  another  substance.  The  amount 
of  friction  depends  upon  the  pressure  between  the  surfaces  in 
contact. 

When  work  is  done  a  part  of  the  energy  which  is  put  into 
it  is  naturally  lost.  In  the  case  of  water  this  is  due  to  the 
friction.  All  the  power  which  the  water  has  cannot  be  used 
to  advantage,  and  efficiency  is  the  ratio  of  the  useful  work  done 
by  the  water  to  the  total  work  done  by  it. 

Efficiency.  —  To  find  the  work  done  upon  the  water  when  a 
pump  lifts  or  forces  it  to  a  height,  multiply  the  weight  of  the 
water  by  the  height  through  which  it  is  raised. 

Since  friction  must  be  taken  into  consideration,  the  useful 
work  done  upon  the  water  when  the  same  power  is  exerted 
will  equal  the  weight  of  the  water  multiplied  by  the  height 
through  which  it  is  raised,  multiplied  by  the  efficiency  of  the 
pump. 

EXAMPLE.  —  Find  the  power  required  to  raise  half  a  ton 


354       VOCATIONAL  MATHEMATICS  FOR   GIRLS 

(long  ton,  or  2240  Ib.)  of  water  to  a  height  of  40  feet,  when 
the  efficiency  of  the  purnp  is  75  % . 

Total  work  done  =  weight  x  height  x  efficiency  counter 
1120  x  40  x  V?°  =  59,733.3  ft.  Ib. 

H.  P.  required  =  59^733-3  =  1.8.     Ana. 
33000 


EXAMPLES 

1.  Find  the  power  required  to  raise  a  cubic  foot  of  water 
28',  if  the  pump  has  80%  efficiency.1 

2.  Find  the  power  required  to  raise  80  gallons  of  water  15', 
if  the  pump  has  75  %  efficiency. 

3.  Find  the  power  required  to  raise  253  gallons  of  water 
18',  if  the  pump  has  70  %  efficiency. 

4.  Find  the  power  required  to  raise  a  gallon  of  water  16',  if 
the  pump  has  85  %  efficiency. 

5.  Find  the  power  required  to  raise  a  quart  of  water  25',  if 
the  pump  has  70  %  efficiency. 

Density  of  Water 

The  mass  of  a  unit  volume  of  a  substance  is  called  its 
density.  One  cubic  foot  of  pure  water  at  39.1°  F.  has  a  mass 
of  62.425  pounds  ;  therefore,  its  density  at  this  temperature  is 
62.425,  or  approximately  62.5.  At  this  temperature  water 
has  its  greatest  density.  With  a  change  of  temperature,  the 
density  is  also  changed. 

With  a  rise  of  temperature,  the  density  decreases  until  at 
212°  F.,  the  boiling  point  of  water,  the  weight  of  a  cubic  foot 
of  fresh  water  is  only  59.64  pounds. 

When  the  temperature  falls  below  39.1°  F.,  the  density  of 
water  decreases  until  we  find  the  weight  of  a  cubic  foot  of  ice 
to  be  but  57.5  pounds. 
1  Consider  the  time  1  minute  in  all  power  examples  where  the  time  is  not  given. 


PLUMBING  AND   HYDRAULICS  355 

EXAMPLES 

1.  One  cubic  foot  of  fresh  water  at  62.5°  F.  weighs  62.355  lb., 
or  approximately  62.4  lb.    What  is  the  weight  of  1  cubic  inch  ? 
What  is  the  weight  of  1  gallon  (231  cubic  inches)  ? 

2.  What  is  the  weight  of  a  gallon  of  water  at  39.1°  F.  ? 

3.  What  is  the  weight  of  a  gallon  of  water  at  212°  F.  ? 

4.  What  is  the  weight  of  a  volume  of  ice  represented  by  a 
gallon  of  water  ? 

5.  What  is  the  volume  of  a  pound  of  water  at  ordinary 
temperature,  62.5°  F.  ? 

Specific  Gravity 

Some  forms  of  matter  are  heavier  than  others,  i.e.  lead  is 
heavier  than  wood.  It  is  often  desirable  to  compare  the 
weights  of  different  forms  of  matter  and,  in  order  to  do  this, 
a  common  unit  of  comparison  must  be  selected.  Water  is 
taken  as  the  standard. 

Specific  Gravity  is  the  ratio  of  the  mass  of  any  volume  of  a 
substance  to  the  mass  of  the  same  volume  of  pure  water  at 
4°  C.  or  39.1°  F.  It  is  found  by  dividing  the  weight  of  a  known 
volume  of  a  substance  in  liquiqL  by  the  weight  of  an  equal 
volume  of  water. 

EXAMPLE.  —  A  cubic  foot  of  wrought  iron  weighs  about 
480  pounds.  Find  its  specific  gravity. 

NOTE.  —  1  eu.  ft.  of  water  weighs  62.425  lb. 

Weight  of  1  cu.  ft.  of  iron    _    480    _  ,-  -        , 
Weight  of  1  cu.  ft.  of  water  ~  62.425 

To  find  Specific  Gravity. — To  find  the  specific  gravity  of  a 
solid,  weigh  it  in  air  and  then  in  water.  Find  the  difference 
between  its  weight  in  air  and  its  weight  in  water,  which  will 
be  the  buoyant  force  on  the  body,  or  the  weight  of  an  equal 
volume  of  water.  Divide  the  weight  of  the  solid  in  air  by  its 
buoyant  force,  or  the  weight  of  an  equal  volume  of  water,  and 
the  quotient  will  be  the  specific  gravity  of  the  solid. 


356        VOCATIONAL  MATHEMATICS  FOR   GIRLS 

Tables  have  been  compiled  giving  the  specific  gravity  of  different  solids, 
so  it  is  seldom  necessary  to  compute  it. 

The  specific  gravity  of  liquids  is  very  often  used  in  the 
industrial  world,  as  it  means  the  "  strength  "  of  a  liquid.  In 
the  carbonization  of  raw  wool,  the  wool  must  be  soaked  in 
sulphuric  acid  of  a  certain  strength.  This  acid  cannot  be 
bought  except  in  its  concentrated  form  (sp.  gr.  1.84),  and  it 
must  be  diluted  with  water  until  it  is  of  the  required  strength. 

The  simplest  way  to  determine  the  specific  gravity  of  a  liquid  is  with 
a  hydrometer.  This  instrument  consists  of  a  closed  glass  tube,  with  a 
bulb  at  the  lower  end  filled  with  mercury.  This  bulb  of  mer- 
cury keeps  the  hydrometer  upright  when  it  is  immersed  in  a 
liquid.  The  hydrometer  has  a  scale  on  the  tube  which  can 
be  read  when  the  instrument  is  placed  in  a  graduate  of  the 
liquid  whose  specific  gravity  is  to  be  determined. 

But  not  all  instruments  have  the  specific  gravity  recorded 
on  the  stem.  Those  most  commonly  in  use  are  graduated 
with  an  impartial  scale. 

In  England,  Twaddell's  scale  is  commonly  employed,  and 
since  most  of  the  textile  mill  workers  are  English,  we  find  the 
same  scale  in  use  in  this  country.  The  Twaddell  scale  bears  a 
marked  relation  to.  specific  gravity  and  can  be  easily  converted 
into  it. 

Another  scale  of  the  hydrometer  is  the  Beaume,  but  these 
readings  cannot  be  converted  into  specific  gravity  without 
the  use  of  a  complicated  formula  or  reference  to  a  table.  ^  ••  -^ 

HYDROMETER  SCALE  FORMULA  FOR  CONVERTING  INTO  S.  G. 

1.  Specific  gravity  hydrometer  Gives  direct  reading 

2.  Twaddell  g  G  =  (.5  x  ^)  +  100 

100 


3.  Beaume  S.  G.  = 


N=  the  particular  degree  which  is  to  be  converted. 
EXAMPLE.  —  Change  168  degrees  (Tw.)  into  S.  G. 


=L84> 
100 


PLUMBING  AND   HYDRAULICS  357 

Another  formula  for  changing  degrees  Twaddell  scale  into  specific 
gravity  is  :  (5  x  JV)  +  1000  =  gpecific  gravitVi 

1000 

In  Twaddell's  scale,  1°  specific  gravity  =  1.005 
2°  specific  gravity  =  1.010 
3°  specific  gravity  =  1.015 

and  so  on  by  a  regular  increase  of  .005  for  each  degree. 

To  find  the  degrees  Twaddell  when  the  specific  gravity  is  given,  multi- 
ply the  specific  gravity  by  1000,  subtract  1000,  and  divide  by  5.  Formula  : 

(S.G.X  1000) -1000  =  degrees  T^^H 
5 

EXAMPLE.  —  Change  1.84  specific  gravity  into  degrees  Twad- 
dell, 

(1.84x1000) -1000  =  16g  degrees  Twadden 
5 

EXAMPLES 

1.  What  is  the  specific  gravity  of  sulphuric  acid  of  116°  Tw.? 

2.  What  is  the  specific  gravity  of  acetic  acid  of  86°  Tw.  ? 

3.  What  is  the  specific  gravity  of  a  liquid  of  164°  Be.  ? 

4.  What  is  the  specific  gravity  of  a  liquid  of  108°  Be.  ? 

5.  What  is  the  specific  gravity  of  a  liquid  of  142°  Tw.? 

Heat 

Heat  Units.  —  The  unit  of  heat  used  in  the  industries  and 
shops  of  America  and  England  is  the  British  TJiermal  Unit 
(B.  T.  U.)  and  is  defined  as  the  quantity  of  heat  required  to 
raise  one  pound  of  water  through  a  temperature  of  one  degree 
Fahrenheit.  Thus  the  heat  required  to  raise  5  Ib.  of  water 
through  15  degrees  F.  equals 

5  x  15  =  75  British  Thermal  Units  (B.  T.  U.) 
Similarly,  to  raise  86  Ib.  of  water  through  £°  F.  requires 
86  x  i  =  43  B.  T.  U. 

The  unit  used  on  the  Continent  and  by  scientists  in  America 
is  the  metric  system  unit,  a  calorie.  This  is  the  amount  of 
heat  necessary  to  raise  1  gram  of  water  1  degree  Centigrade. 


358       VOCATIONAL  MATHEMATICS  FOR   GIRLS 


EXAMPLES 

1.  How  many  units   (B.   T.   U.)  will  be  required  to  raise 
4823  Ib.  of  water  62  degrees  ? 

2.  How  many  B.  T,  U.  of  heat  are  required  to  change  365 
cubic  feet  of  water  from  66°  F.  to  208°  F.? 

3.  How  many  units  (B.  T.  U.)  will  be  required  to  raise  785 
Ib.  of  water  from  74°  F.  to  208°  F.? 

(Consider  one  cubic  foot  of  water  equal  to  621  lb.) 

4.  How  many  B.  T.  U.  of  heat  are  required  to  change  1825 
cu.  ft.  of  water  from  118°  to  211°  ? 

5.  How  many  heat  units  will  it  take  to  raise  484  gallons  of 
water  12  degrees  ? 

6.  How  many  heat  units  will  it  take  to  raise  5116  gallons 
of  water  from  66°  F.  to  198°  F.? 

Temperature 

The  ordinary  instruments  used  to  measure  temperature 
are  called  thermometers.  There  are  two  kinds  —  Fahren- 
heit and  Centigrade.  The  Fahrenheit  ther- 
mometer consists  of  a  cylindrical  tube  filled 
with  mercury  with  the  position  of  the  mercury 
at  the  boiling  point  of  water  marked  212,  and  the 
position  of  mercury  at  the  freezing  point  of 
water  32.  The  intervening  space  is  divided  into 
180  divisions.  The  Centigrade  thermometer  has 
the  position  of  the  boiling  point  of  water  100 
and  the  freezing  point  0.  The  intervening  space 
is  divided  into  100  spaces.  It  is  often  necessary 
to  convert  the  Centigrade  scale  into  the  Fah- 
renheit scale,  and  Fahrenheit  into  Centigrade. 

To  convert  F.  into  C.,  subtract  32  from  the  F. 
degrees  and  multiply  by  -|,  or  divide  by  1.8,  or 
C.  =  (F.  -  32°)  f ,  where  C.  =  Centigrade  reading 
and  F.  =  Fahrenheit  reading. 


100 


O 


17.8 


THERMOMETERS 


2121 


HEAT  AND   TEMPERATURE  359 

To  convert  C.  to  F.,  multiply  C.  degrees  by  f  or  1.8  and  add 
32°. 


5 
EXAMPLE.  —  Convert  212  degrees  F.  to  C.  reading 

5(212°-  32  ")      5(180°)      900° 

-*  =•  -  •  =  luu    v_y. 
9  99 

EXAMPLE.  —  Convert  100  degrees  C.  to  F.  reading. 

9  x  100°  +  32°  =  —  +  32°  =  180°  +  32°  =  212°  F. 
5  5 

If  the  temperature  is  below  the  freezing  point,  it  is  usually 
written  with  a  minus  sign  before  it  :  thus,  15  degrees  below  the 
freezing  point  is  written  —  15°.  In  changing  —  15°  C.  into  F. 
we  must  bear  in  mind  the  minus  sign. 


Thus,      Jp  =  -+320      ^=~  +  32°  =-27°  +  32°  =5° 

5  5 

EXAMPLE.  —  Change  -  22°  F.  to  C. 

C.  =  f  (F.  -  32) 

C.  =  f  (-  22°  -  32°)  =  $  (  -  54°)  =  -  30° 

EXAMPLES 

1.  Change  36°  F.  to  C.  6.  Change  225°  C.  to  F. 

2.  Change  89°  F.  to  C.  7.  Change  380°  C.  to  F. 

3.  Change  289°  F.  to  C.  8.  Change  415°  C.  to  F. 

4.  Change  350°  F.  to  C.  9.  Change  580°  C.  to  F. 

5.  Change  119°  C.  to  F. 

Latent  Heat 

By  latent  heat  of  water  is  meant  that  heat  which  water  ab- 
sorbs in  passing  from  the  liquid  to  the  gaseous  state,  or  that 
heat  which  water  discharges  in  passing  from  the  liquid  to  the 


360       VOCATIONAL  MATHEMATICS  FOR   GIRLS 

solid  state,  without  affecting  its  own  temperature.  Thus,  the 
temperature  of  boiling  water  at  atmospheric  pressure  never 
rises  above  212  degrees  F.,  because  the  steam  absorbs  the 
excess  of  heat  which  is  necessary  for  its  gaseous  state.  Latent 
heat  of  steam  is  the  quantity  of  heat  necessary  to  convert  a 
pound  of  water  into  steam  of  the  same  temperature  as  the 
steam  in  question. 

COMMERCIAL  ELECTRICITY 

Amperes.  —  What  electricity  is  no  one  knows.  Its  action, 
however,  is  so  like  that  of  flowing  water  that  the  comparison  is 
helpful.  A  current  of  water  in  a  pipe  is  measured  by  the 
amount  which  flows  through  the  pipe  in  a  second  of  time,  as 
one  gallon  per  second.  So  a  current  of  electricity  is  measured 


WATER  ANALOGY  OF  FALL  OF  POTENTIAL 

by  the  amount  which  flows  along  a  wire  in  a  second,  as  one 
coulomb  per  second,  —  a  coulomb  being  a  unit  of  measurement 
of  electricity,  just  as  a  gallon  is  a  unit  of  measurement  of 
water.  -The  rate  of  flow  of  one  coulomb  per  second  is  called  one 
ampere.  The  rate  of  flow  of  five  coulombs  per  second  is  five 
amperes. 

Volts.  —  The  quantity  of  water  which  flows  through  a  pipe 
depends  to  a  large  extent  upon  the  pressure  under  which  it 
flows.  The  number  of  amperes  of  electricity  which  flow  along 
a  wire  depends  in  the  same  way  upon  the  pressure  behind  it. 


COMMERCIAL  ELECTRICITY  361 

The  electrical  unit  of  pressure  is  the  volt.  In  a  stream  of 
water  there  is  a  difference  in  pressure  between  a  point  on  the 
surface  of  the  stream  and  a  point  near  the  bottom.  This  is 
called  the  difference  or  drop  in  level  between  the  two  points. 
It  is  also  spoken  of  as  the  pressure  head,  "  head  "  meaning  the 
difference  in  intensity  of  pressure  between  two  points  in  a  body 
of  water,  as  well  as  the  intensity  of  pressure  at  any  point. 
Similarly  the  pressure  (or  voltage)  between  two  points  in  an 
electric  circuit  is  called  the  difference  or  drop  in  pressure  or 
the  potential.  The  amperes  represent  the  amount  of  electricity 
flowing  through  a  circuit,  and  the  volts  the  pressure  causing 
the  flow. 

Ohms.  —  Besides  the  pressure  the  resistance  of  the  wire 
helps  to  determine  the  amount  of  the  current  :  —  the  greater 
the  resistance,  the  less  the  current  flowing  under  the  same 
pressure.  The  electrical  unit  of  resistance  is  called  an  ohm. 
A  wire  has  a  resistance  of  one  ohm  when  a  pressure  of  one  volt 
can  force  no  more  than  a  current  of  one  ampere  through  it. 

Ohm's  Law.  —  The  relation  between  current  (amperes), 
pressure  (volts),  and  resistance  (ohms)  is  expressed  by  a  law 
known  as  Ohm's  Law.  This  is  the  fundamental  law  of  the 
study  of  electricity  and  may  be  stated  as  follows  : 

An  electric  current  flowing  along  a  conductor  is  equal  to 
the  pressure  divided  by  the  resistance. 


Current  (amperes)  ^  (volts 


Resistance  (ohms) 
Letting  /=  amperes,  E  =  volts,  R  =  ohms, 


I=E  +  Rm  /  =  - 
R 

E=  IR 


EXAMPLE.  —  If  a  pressure  of  110  volts  is  applied  to  a  re- 
sistance of  220  ohms,  what  current  will  flow  ? 


362       VOCATIONAL  MATHEMATICS  FOR   GIRLS 

/  =  —  =  —  =  -  =  .5  ampere.     Ans. 
E     220     2 

EXAMPLE. — A  current  of  2  amperes  flows  in  a  circuit  the  resist- 
ance of  which  is  300  ohms.  What  is  the  voltage  of  the  circuit  ? 

IE  =  E 

2  x  300  -  600  volts.     Ans. 

EXAMPLE.  —  If  a  current  of  12  amperes  flows  in  a  circuit 
and  the  voltage  applied  to  the  circuit  is  240  volts,  find  the 
resistance  of  the  circuit. 

^  =  E     ?40  _  2Q  ohms_    Ans 
I  12 

Ammeter  and  Voltmeter.  —  Ohm's  Law  may  be  applied  to  a 
circuit  as  a  whole  or  to  any  part  of  it.  It  is  often  desirable  to 

know  how  much  current  is  flowing 
in  a  circuit  without  calculating  it  by 
Ohm's  Law.  An  instrument  called 
an  ammeter  is  used  to  measure  the 
current.  This  instrument  has  a 
low  resistance  so  that  it  will  not 
cause  a  drop  in  pressure.  A  volt- 
meter is  used  to  measure  the  voltage. 
This  instrument  has  high  resistance 
so  that  a  very  small  current  will 

flow  through  it,  and  is  always  placed  in  shunt,  or  parallel 
(see  p.  235)  with  that  part  of  the  circuit  the  voltage  of  which 
is  to  be  found. 

EXAMPLE.  —  What  is  the  resistance  of  wires  that  are  carry- 
ing 100  amperes  from  a  generator  to  a  motor,  if  the  drop  or 
loss  of  potential  equals  12  volts  ? 

Drop  in  voltage  =  IE  1=  100  amperes 

Drop  in  volts      =12  E  =      ?  ohms 

E=—  E=  —  =  0.12  ohm.     Ans. 

EXAMPLE.  —  A  circuit  made  up  of  incandescent  lamps  and 
conducting  wires  is  supplied  under  a  pressure  of  115  volts. 


COMMERCIAL  ELECTRICITY 


363 


The  lamps  require  a  pressure  of  110  volts  at  their  terminals 
and  take  a  current  of  10  amperes.  What  should  be  the  resist- 
ance of  the  conducting  wires  in  order  that  the  necessary  cur- 
rent may  flow  ? 

Drop  in  conducting  wires  =  115  —  110  =  5  volts 

Current  through  wires       =    10  amperes 

It  =  —  —  —  =  0.5  ohm  resistance.     Ans. 

EXAMPLES 

1.  How  much  current  will  flow  through  an  electromagnet 
of  140  ohms'  resistance  when  placed  across  a  100-volt  circuit  ? 

2.  How  many  amperes  will  flow  through  a  110-volt  lamp 
which  has  a  resistance  of  120  ohms  ? 

3.  What  will   be   the   resistance  of   an  arc  lamp   burning 
upon  a  110-volt  circuit,  if  the  current  is  5  amperes  ? 

4.  If  the  lamp  in  Example  3  were  to  be  put  upon  a  150-volt 
circuit,  how  much  additional  resistance  would  have  to  be  put 
into  it  in  order  that  it  might  not  take  more  than  5  amperes  ? 


11 

Fc-ed  Wire                  ^ 

§ 

<  } 

A^               -f- 

Trolley  Wire/ 

Dynamo 


ELECTRIC  ROAD  SYSTEM 

5.  In  a  series  motor  used  to  drive  a  street  car  the  resistance 
of  the  field  equals  1.06  ohms  ;  the  current  going  through  equals 
30  amperes.      What   would   a   voltmeter   indicate   if    placed 
across  the  field  terminals  ? 

6.  If  the  load  upon  the  motor  in  Example  5  were  increased 
so  that  45  amperes  were  flowing  through  the  field  coils,  what 
would  the  voltmeter  then  indicate  ? 


INDEX 


Addition,  3 

Compound  numbers,  46 

Decimals,  33 

Fractions,  21 
Aliquot  parts,  39 
Alkalinity  of  water,  298 
Ammeter,  362 
Ammonia,  296 
Amount,  53 
Amperes,  169,  360 
Angles,  66 

Complementary,  66 

Right,  66 

Straight,  66 

Supplementary,  66 
Annuity,  192 
Antecedent,  37 
Apothecary's  weights,  276 
Apothem,  72 

Approximate  equivalents  between 
metric  and  household  measures, 
281 

Approximate  measures  of  fluids,  277 
Arc,  64 

Area  of  a  ring,  65 
Area  of  a  triangle,  69 
Atmospheric  pressure,  349 
Avoirdupois  weight,  43 


Bacteria,  294,  298 
Banks,  178 

Cooperative,  179 

National,  178 

Savings,  179 
Baths,  292 
Bed  linen,  161 
Beef,  118 
Bills,  243 

Blue  print  reading,  80 
Board  measure,  131 
Bonds,  187 
Brickwork,  134 


Building  materials,  133 
Buying  Christmas  gifts,  94 

Cotton,  229 

Rags,  229 

Wool,  229 

Yarn,  229 


Cancellation,  13 
Capacity  of  pipes,  348 
Carbohydrates,  102 
Cement,  136 
Chlorine,  297 
Circle,  64 
Circumference,  64 
Civil  Service,  268 
Claims,  196 
Clapboards,  138 
Clothing,  91 
Coefficients,  331 
Color  of  water,  296 
Common  denominator,  20 

Fractions,  17 

Multiple,  15 

Comparative      costs      of      digestible 
nutrients  and  energy  in  different 
food  materials  at  average  prices, 
114,  115 
Compound  numbers,  42,  46 

Addition,  46 

Division,  47 

Multiplication,  47 

Subtraction,  46 

Computing  profit  and  loss,  252 
Cone,  75 
Consequent,  57 
Construction  of  a  house,  128 
Cooperative  banks,  179 
Cost  of  food,  105 
Cost  of  furnishing  a  house,  146 
Cost  of  subsistence,  91 
Cotton,  217 

Yarns,  223 
365 


366 


INDEX 


Counting,  44 
Credit  account,  244 
Cube,  61 
Cube  Root,  61 
Cubic  measure,  42 
Cuts  of  Beef,  120 

Mutton,  122 

Pork,  121 
Cylindrical  tank,  347 

Dairy  Products,  310 

Debit,  244 

Decimal  Fractions,  30 

Addition,  33 

Division,  36 

Mixed,  31 

Multiplication,  35 

Reduction,  32 

Subtraction,  34 
Denominate  fraction,  45 

Number,  42,  45 
Denomination,  42 
Denominator,  17 
Density  of  water,  354 
Deodorants,  294 
Diameter,  64 

Distribution  of  income,  89 
Division,  9 

Compound  numbers,  47 

Fractions,  25 

Income,  92 
Drawing  to  scale,  85 
Dressmaking,  198 
Dry  measure,  43 

Economical  marketing,  125 

Uses  of  Meats,  117 
Economy  of  space,  130 
Efficiency  of  water,  353 
Electricity,  360 
Ellipse,  72 
English  system,  276 
Ensilage  problems,  307 
Equations,  332 

Substituting,  334 

Transposing,  334 
Equiangular  triangle,  68 
Equilateral  triangle,  68 
Estimating  distances,  86 

Weights,  87 
Evolution,  61 


Exchange,  193 

Expense  account  book,  95 

Factors,  13 

Farm  measures,  307 

Problems,  305 
Filling,  217 
Flax,  217 
Flooring,  139 
Fluid  measure,  277 
Food,  100 

Values,  110 
Formulas,  327 

For  computing  profit  and  loss,  253 
Fractions,  17 

Addition,  21 

Common,  17 

Decimal,  30 

Division,  25 

Improper,  17 

Multiplication,  24 

Reduction,  17 

Subtraction,  22 
Frame  and  roof,  132 
Free  ammonia,  297 
Frustum  of  a  cone,  76 
Furnishing  a  bedroom,  153,  154,  155 

Dining  room,  156 

Hall,  146 

Kitchen,  162 

Living  room,  149,  150,  152 

Sewing  room,  161 

Germicides,  294 

Graphs,  322 

Greatest  common  divisor,  15 


Hardness  of  water,  298 
Heat,  357 

And  light,  167 

Units,  357 
Hem,  200 
Hexagon,  72 
Horizontal  addition,  237 
Household  linens,  160 

Measures,  277 
How  to  make  change,  266 

Solutions  of  various  strengths  from 
crude  drugs  or  tablets  of  known 
strength,  286 


INDEX 


367 


How  to  read  an  electric  meter,  169 

Gas  meter,  168 
Hypodermic  doses,  288 

Improper  fractions,  17 
Inclined  planes,  344 
Income,  89 

Inside  area  of  tanks,  348 
Insurance,  188 

Fire,  188 

Life,  189 

Integer,  1,  17,  31,  45 
Interest,  53 

Compound,  56 

Simple,  53 
Interpretation  of  negative  quantities, 

337 

Invoice  bills,  243 
Involution,  61 
Iron  in  water,  298 
Isosceles  triangle,  68 

Jack  screw,  344 

Kilowatt,  169 

Kitchen  weights  and  measures,  103 

Latent  heat,  359 

Lateral  pressure,  351 

Lathing,  141 

Law  of  squares,  348 

Least  common  multiple,  15 

Ledger,  244 

Levers,  344 

Linear  measure,  42 

Linen,  217 

Yarns,  222 
Liquid  measure,  43 
Lumber,  131 

Machines,  344 
Measure,  of  time,  43 

Length,  317 
Medical  chart,  292 
Mensuration,  64 
Menus,  making  up,  113 
Merchandise,  243 
Methods  of  heating,  174 
Methods    of   solving    examples,    87, 

88 
Metric  system,  276,  279,  282,  317-319 


Millinery  problems,  212 
Mixed  decimals,  31 
Mohair,  217 
Momentum,  342 
Money  orders,  194 
Mortar,  133 
Mortgages,  180 
Motion,  342 
Multiplication,  8,  242 

Algebraic  expressions,  339 

Compound  numbers,  47 

Decimals,  31 

Fractions,  24 
Mutton,  122,  123 

National  banks,  178 

Nitrogen,  297 

Notation,  1 

Notes,  181 

Numerals,  Roman,  2 

Numeration,  1 

Numerator,  17 

Nurses,  arithmetic  for,  276-303 

Nutritive  ingredients  of  food,  101 

Octagon,  72 

Odor  of  water,  296 

Ohm,  361 

Ohm's  Law,  361 

Oxygen  consumed,  297 

Painting,  141 
Papering,  142 
Paper  measure,  44 
Pay  rolls,  255 
Pentagon,  72 
Percentage,  50 
Perimeter,  72 
Plank,  131 
Plastering,  133 
Polygons,  72 
Poultry  problems,  312 
Power,  30 
Pressure,  lateral,  351 

Per  square  inch,  350 

Water,  350 
Principal,  53 
Profit  and  loss,  246 
Promissory  notes,  182 
Proper  fractions,  17 
Proportion,  57,  58,  59 


368 


INDEX 


Protractor,  67 
Pulleys,  344 
Pyramid,  75 

Quadrilaterals,  71 

Radius,  64 

Rapid  calculation,  233 

Rate  (per  cent),  50 

Ratio,  57 

Raw  silk  yarns,  222 

Reading  a  blue  print,  80 

Rectangle,  71 

Reduction,  42 

Ascending,  42,  44 

Descending,  42,  44 
Right  triangles,  68,  69 
Roman  numerals,  2 
Root,  cube,  62 

Square,  61 
Ruffles,  201 
Rule  of  thumb  methods,  88 

Savings  bank,  179 

Interest  tables,  56 
Scalene  triangle,  68 
Sector,  64 

Sediment  in  water,  296 
Shingles,  137 
Shoes,  219 
Silk,  217 
Similar  figures,  77 

Terms,  331 
Simple  interest,  53 

Proportion,  59 
Slate  roofing,  137 
Specific  gravity,  355 
Specimen  arithmetic  papers,  272 

Sealers  of  Weights  and  Measures, 
273 

State  visitors,  274 

Stenographers,  273 
Sphere,  76 
Spun  silk  yarns,  223 
Square  measure,  42 
Square  root,  62 
Stairs,  140 
Steers  and  beef,  118 
Stocks,  184 
Stonework,  135 
Strength  of  solutions,  224 


Studding,  132 

Substituting  in  equations,  334 

Subtraction 

Compound  numbers,  46 

Decimals,  34 

Fractions,  22 
Supplement,  66 

Table  linen,  161 

Table  of  metric  conversion,  317 

Table  of  wages,  257 
Tanks,  347 
Taxes,  143 

Temperature,  290,  358 
Temporary  loans,  259 
Terms  used  in  chemical  and  bacterio- 
logical reports,  296 
Time  and  speed,  341 
Time  sheets,  255 
Trade  discount,  52,  207 
Transposing  in  equations,  334 
Trapezium,  71 
Trapezoid,  72 
Triangles,  68 

Equiangular,  68 

Equilateral,  68 

Isosceles,  68 

Right,  68,  69 

Scalene,  68 
Trust  companies,  179 
Tucks,  199 

Turbidity  of  water,  296 
Two-ply  yarns,  223 

Unit,  1 

United  States  revenue,  144 

Useful  mechanical  information,  341 

Use  of  tables,  88 

Uses  of  nutrients  in  the  body,  102 

Value  of  coal  to  produce  heat,  167 
Volt,  169,  360 
Voltmeter,  362 
Volume,  74 

Warp,  217 

Water,  alkalinity  of,  298 

Ammonia  in,  296,  297 

Analysis  of,  296 

Bacteria  in,  298 

Chlorine  in,  297 


INDEX 


369 


Water,  s —  continued. 
Color  of,  296 
Hardness  of,  298 
Iron  in,  298 
Nitrogen  in,  297 
Odor  of,  296 

Oxygen  consumed  by,  297 
Power,  353 
Pressure,  350 

Residue  on  evaporation,  296 
Sediment  in,  296 
Supply,  345 
Traps,  352 
Turbidity  of,  296 


Watt,  170 
Wool,  211 
Woolen  yarns,  220 
Work,  343 
Worsted  yarns,  219 

Yarns,  217 
Cotton,  223 
Linen,  222 
Raw  silk,  222 
Spun  silk,  223 
Two-ply,  223 
Woolen,  220 
Worsted,  219 


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